Nah, actually I don't own the game (but played it for few hours at a friend's place). I've skipped it for that very reason. A great game, just too bad its not polished the way it deserves to be.
I was a little involved in the development of the "Unofficial Oblivion Patch", and I am telling you, lots, lots of things (more like thousands) were left as they are. Bethesda didn't care, and still doesn't, because the way they see it, if you do everything the way their way, the main quest will get done. About the others, well, "you did something wrong". :D There were many quest scripts wrong with Oblivion, and lots of times the quests will get screwed up.
I understand it is a different game, but it uses the same engine and was developed pretty much the same way, so the same kind of issues still exist here.

Actually that's not completely true, it's a little more tricky than that.
Only original version found on the DVD is really DRM-free, all the other version will contains DRM, which means that sure you can install the game offline but as soon as you update it the standard Stardock DRM will be installed that will require you to reactivate the game online if you ever change something significant on your hardware or if you try to copy the game to another PC (exactly like the Steam offline mode) and the same goes for all other Stardock games.

And once the game is updated, it's still protection free. So if you're really paranoid, you can just back up your Demigod folder. And voila, instant fully patched DRM free game.

Because we all get our patches from where again? Oh yeah! The internet.

Sorry, but I'm not seeing your point - or at least not what it has to do with what I said.

The key difference is that a standalone patch can be mirrored across dozens of sites, with few of them even officially associated with the company producing the game, while with a system such as Impulse the patch has to be kept available by whatever company owns the client and the patch cannot be mirrored or stored by independent groups.

My point is that, yes, patching requires you to connect to the internet... just like every other game. The only difference is that it's all provided through one client rather than trawling through various sites trying to find one that not only has the patch, but offers it at a half decent speed. Oh and doesn't have you waiting in a queue for half an hour. That's good too.
Add to that the fact that you don't have to try and find out which patches you need, whether they're applicable to your regional version and what order to install them all in and being able to use Impulse to handle all the patching automatically starts to look like a blessing, not a DRM-ridden curse.

Patching being integrated into a game's launcher or into a client can certainly have the advantages you mentioned, but unless there are also standalone patches provided it also means that at some point in the future it won't be possible to patch the game anymore. I know I own quite a few games with patching integrated into the launchers, but where the servers containing those patches are no longer online, and if it weren't for standalone patches also being released I'd be stuck with the out-of-the-box version of those games.

Which is as far as they take the copy protection. If a GOG game needed an update it would have to be updated through GOG as downloading from anywhere else would see your copy start asking for a CD/DVD you don't have. Yet nobody debates GOG's DRM free status, despite the fact that you're equally reliant on GOG as the one and only source of (legal) updates. And yes, GOG games have needed to be updated.
Also, as stated above, not having to trawl through independent sites is beneficial in many ways anyway.

Equally, I know of many games whose patches have disappeared from the 'net despite the fact that they were never tied to an online service. It's the way things go. It's also why I keep an extremely substantial amount of patches backed up.

Exactly, which only emphasizes the importance of having standalone patches available, so they can be mirrored both on the internet and also stored locally. Flexibility and options are the key, and that is what tying patches to a client takes away. Now, this is obviously a very minor complaint, but still something that should be kept in mind.

whoa...I didn't know this. I hope this won't happen to fan patches, yes?

This assumes the game in question has DRM/Copy Protection that requires the disc in the drive. But in all likelihood, this would happen, as the updated executable would contain the DRM and then you'd be stuck with a game that wants a disc in the drive. Of course, since you have a backup of your original GOG DL (either self-created or on your GOG shelf), you can always reinstall the GOG version and forget the patch.

I wouldn't worry about that too much. Most games here are done in terms of patching, and in the strange event that it wasn't, I'm sure GoG would recognize it and update it as needed.