If gamersgate ever does that it will probably mean we are going through the Apocalypse, so, fuck that.

Taking away my right to redownload or update the game is not the same as taking away the game.
If you purchase a game at retail, do you expect them (or the publisher) to reissue the game to you in the future at no extra charge? If they provided that service, would it be DRM? What if they asked for a receipt?
If the developer goes out of business, do you still expect updates to your retail game? (Of course, patches usually aren't tied to an account).
If GOG used a fire-and-forget payment model - you buy once, and what you get is all you get - would that still count as being able to take away my games? This is precisely a subset of what they currently do.

That's analogous to throwing out your retail disc after you install the game, though. GOG is not installing the game for you, they're just selling you the installation files. It's not GOG's fault if you delete what you purchased.
GOG is peculiar in this case, because not only are they the distributor and the developer (in that any updates made to the products sold here are made by GOG, even if it means integrating a new base patch from the real developer), but they don't issue patches at all; they only update the installation files, so the updates are inseparable from the base product. Thus, if GOG goes out of business, it's our responsibility to first ensure that our products are up-to-date, as the updates simply don't exist on their own.
However, it's true that your account could be disabled and the game later updated, which would prevent you from getting that update.

Look into how Impulse and Steam handle things. They pretty much follow the exact same model as GoG (well, other way around, but you know what I mean). Hell, Company of Heroes is notorious for how you have to redownload everything for every single DD patch.

Maybe, but we're getting off-track. I'm not going to take the position that GOG is DRM-free for all definitions of DRM (that would be silly), and I don't have much to say about Impulse at the moment. I just took issue with the claim that GOG can take away your games at will.

Well, that IS true, but only in the sense that any DD service can. It is even in the EULA/TOS/whatever. It just becomes a question of how effective it would be (GoG, GG, and Impulse let you make archives, and I think Impulse's is GOO-free) coupled with how incredibly unlikely it would be (even "The Big Evil Steam" will probably never do it, without good reason).
Personally, I see it as a non-issue. I just mention it since so many people run around saying you are "renting" games because other services can do this. So I like to give them the finger by pointing out that GoG can too :p

I see the point you are making, but I think you should preface your claims with "in my opinion", because not everyone will agree with your definition.
To my mind, systems that restrict how you obtain the game are not DRM, while systems that artificially restrict how you may use the game or the installer once you have obtained it are DRM.
If the downloaded installer can be copied and reused to your heart's content, it is DRM-free. If there are artificial restrictions in place on where, how or when you may install or run the game, it probably is DRM-protected. Hence, GOG's games are DRM-free while your typical SecuROM protected GamersGate game is not.
...in my opinion.

Not everyone agrees with fact, so why should I bother marking things that are my opinion? :p
That being said, I think GoG counting as having DRM is closer to fact than opinion.
Let's use YOUR system, for example. Okay, no restrictions after obtaining it? So any game on a DD service with patches have DRM :p.
Or do we not count patches? If so, Steam can be argued for DRM-free with Offline Mode. And Impulse becomes the definition of DRM-free, since that doesn't force you to update or use the client at all after you obtain it.
Like I said, once you start trying to find that exact thing which defines GoG as DRM-free, you start grasping at straws (in my opinion :p). I still won't get too bothered if people say it is DRM-free, just so long as they aren't also advocating that everything in the world needs to be 100% DRM-Free (because then the chance of mocking them is too high for me to resist :p).

Well, Gamersgate backups require you to log in before you can install them. It's not just the first time you download the game. You can easily rip that out, yes, but circumvention doesn't disprove intent.
Impulse can install from a backup while offline, but I'm not sure how far that goes. If you take a brand-new installation of Windows with no internet connection and install Impulse from a disc, I'm willing to bet it wouldn't help you; you probably need to log in at least once and download your account information. I don't know that for sure, though. If you can just install Impulse and then restore a backup with no account verification required, then sure, it's comparable to GOG (if much more of a hassle), but I'd be surprised if that were the case, given the way that Impulse is set up.
After you download a game from GOG, no further involvement with GOG is required. You have an installer, and that's it. The fact that they store your download history is an additional service, not a means by which to verify your installation. I don't see how you can compare requiring online authentication at install time to not requiring it.

I wouldn't be so quick to label my own opinions as 'fact' -- especially when it is so hard to reliably define the term "DRM".
To my mind my definition still holds, as detailed below. I'll be happy to amend or refine it if necessary though.
Yes, if you are forced to install the patches to be able to play--if the patches are optional, then no.
No;
- You have to be online and logged into your Steam account to be able to enter offline mode. If your internet connection fails or your account is disabled before you enter offline mode, you lose access to your games.
- The offline mode will stop working after a certain period of time (a few months) and you will be forced to go online again and reauthenticate with Steam (I haven't tested this so it might be false).
- You cannot backup your games and install them on a new computer without going through a new authentication (i.e. logging into Steam on that computer) even if you use offline mode on the old computer.
I haven't used Impulse much, but I'm guessing there's a one time online authentication when you first run the game, and you won't be able to transfer the game to a new computer without authenticating again.
There are of course gray areas, but in my opinion GOG is fairly well planted on the "DRM free" side of the fence.
Once I've downloaded a game from GOG, there's no way for GOG to disable my ability to use or reinstall the game in the future. They can delete my account or remove certain games from my account, but that will in no way affect the games I've installed or the installer executables I've downloaded so far. I will still be able to play and reinstall those games and play them on as many computers as I want.
I can of course lose a game if I happen to delete the installer or if my backup fails, but that's my own responsibility and not something someone else is trying to force upon me, and as such I believe it falls outside the scope of DRM.

Has anyone ever actually tried to use the Impulse archive feature? Would probably help :p. Either way, you have to download and authenticate once, but I don't think you necessarily need to authenticate when you install (if you use the magic archive feature that nobody has ever used).
And patches that aren't mandatory? Have you ever played a modern PC game? :p

The way it works is that you select a game from your list and click "download and archive," which does exactly that. When you want to install again, you select "restore from backup" and choose the backup file. This updates the little status indicator next to the game on your list. You can do this while not connected to the internet.
This is why I think it's likely necessary to have an authenticated Impulse installed. Even if you can install Impulse and open it up without having ever logged in, it seems unlikely that the client would let you install a game that isn't on the list, and if you've never logged in, the list is empty. I might test that out later to see what happens.
EDIT:
I just ran an experiment with Mr. Robot. I archived the game, downloaded the Impulse installer, and took my PC offline. I reinstalled Impulse, and was immediately blockaded by a login screen, with no option to enter Impulse with no account information.
I reconnected and logged in, then closed Impulse and disconnected again. Restarting Impulse, I was taken to offline mode, where I was able to restore Mr. Robot from backup. I closed Impulse and was able to launch the game while still offline.
The verdict: as long as you have a functional Impulse client, you can install from backups while offline. However, if your account is disabled, inaccessible or no longer extant, it appears that you cannot launch the client from a clean installation, and thus you cannot install your games. It's also possible that an active client will spaz out if it goes online and can't authenticate your account, or that Impulse will only tolerate being offline for some length of time - I don't know if these things will happen or not.

Once I've downloaded a game from GOG, there's no way for GOG to disable my ability to use or reinstall the game in the future. They can delete my account or remove certain games from my account, but that will in no way affect the games I've installed or the installer executables I've downloaded so far. I will still be able to play and reinstall those games and play them on as many computers as I want.
I can of course lose a game if I happen to delete the installer or if my backup fails, but that's my own responsibility and not something someone else is trying to force upon me, and as such I believe it falls outside the scope of DRM.
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Thats what i would consider DRM free. Any games i have purchased from GOG, D2D and Gamesplanet which are labelled as DRM free have had no restrictions once you have purchased, downloaded & backed them up, which is why i disagree with Gamersgate labelling their games as DRM free when the installer (without using a workaround) needs to access the internet every time you run it.

Agreed, 100%. You can take the installer you download from GOG and create a DRM free backup DVD with it, that will install on any computer without internet access or activation of any kind. This would be the same as going into a store and buying a copy of the game with absolutely no copy protection. You cannot do that with the file you download from GamersGate without a workaround. So I agree that there is a difference.