I registered in 2013 - so you are more "new" than me!
Even then, i'm still a "newbie" compared to some of the original 2007 veterans around here.

Check the link in post 11 ;)

As long as you download the games' offline installers and store them in your drive or hard disk or wherever, then yes, you do own the games. If you just let them stay in your GOG's library (or you delete the offline installers after installing the games), then by the time GOG shuts down, you won't own the games any longer since you've lost your only means of downloading them.

I've noticed that many people do this a lot, and it has always baffled me, and I loathe doing it myself. Not the being new or dormant part, but the part about adding additional qualifiers to queries: I'm such and such a sort of person, and I'm asking my questions for these such reasons. More people should simply just ask the question in my opinion. The rest doesn't help the question to be answered, and no-one else needs to know about me or my motivations but myself. It also makes the inquirer appear timid, out of place, or as if they fear being judged for the question they asked. I am in the same boat as you. This account has been registered for ten years, but only really active for one. I just don't tell people that I'm new, until I open my mouth and remove all doubt, anyway.

But with regards to your question, to at least be a little on topic, as others have stated you can archive the games you purchase. But GOG does not have a complete catalogue of games. As such, you may be interested to know that the following forum posts exist:
https://www.gog.com/forum/general/list_of_drmfree_video_games_digital_distributors/page1
https://www.gog.com/forum/general/list_of_drmfree_games_on_steam/page1
In addition:
https://www.gog.com/forum/general/games_that_treat_gog_customers_as_second_class_citizens_v2/page1
https://www.gog.com/forum/general/drm_on_gog_list_of_singleplayer_games_with_drm/page1
Consider them... additional reading.

Since a growing number of people these days overly question and scrutinize everything people do or say(look at nearly every time a new user posts a thread in these forums, for example), I can sort of see why some do it. That said, I agree with ya.

We don't own anything digital these days, it is all about licenses.

That said, if you compare the status of many games at GOG with games at Steam and other DRM stores, then we here do have a sort of ownership.

We have an ownership, in the sense, that once downloaded and backed up, GOG cannot take them away or anyone else, outside of the courts. And the courts would only do so, if you have transgressed copyright laws (i.e shared them with others who don't have any right to them).

So you might as well say we do own them, but not in the sense where you can legally sell them on.

Basically you own them as much as a game on a disc, aside from selling. Disc or Drive are mostly the same thing. You are allowed to have personal copies, but you cannot copy and give to others.

Strange, the way I remember money working is that the transaction of my wealth to someone else meant that I now own the thing that they once had. This new socialist idea that you can buy something tangible, and yet not own it totally contravenes the basis of a monetary system. Just because some jacka$$ wrote on a piece of paper "you don't own the stuff I'm selling, you only get a license", doesn't make it so. The only reason anyone is letting this trash fly, is because the lawyers making the laws are getting paid big bucks to make laws like this. The "Steam" system goes against the general public's interest. Why am I buying something I don't own? Really dumb.

I have no idea why anyone would support such a system, unless they were in support of the Communist idea that nobody owns anything. So if you like not owning anything, and being happy. I suppose the gulags welcome you, comrade.

Nothing "socialist" about this.
That's capitalism in full swing.

That sounds so "well thought out" and almost convincing, if it wasn't for a fact, that lawyers don't make laws.

There seems to be some confusion as to what that actually means.

You own the license to use something X created. X owns the creation, its copyrights, and the right to exploit it commercially. You owning X's creation would suggest that you have rights to exploit it commercially. You don't. You are paying for the right to use it, and in the case of offline installers, an indefinite license of usage. Whereas with Steam, you're paying for the right to use it as long as Steam is in service.

Both GOG and Steam are selling licenses. They're not selling the rights to the games on offer. Unless you pay the rights holder a considerably larger amount than the one you're paying for on GOG and/or Steam, you don't own the game.

Also, it has nothing to do with communism. In communism, anything created would automatically be part of the public domain. That means: everyone would have rights over it, and there would be no individuality. In a sense, communism is pure democracy in the purest meanings of the word. Capitalism, which is what the selling of products created or the rights to usage of the products created, is what's at fault here.

Lack of education on the topic and misinformation is the true "evil" here, and not labels concerning economic systems.