And even if you had a key you still don't have access to the install media. You could try to extract it from your drive but there is no guarantee that will work on another computer or OS-install since the installer might optionally install what is needed on that computer.
A GoG game comes with a single installer executable (single as in it is the same for everyone, no built in license) that and the resulting game it installs can be freely copied and used on as many machines as you like without any requirements. For example you do not need to have an internet connection or be running the GoG store application.
So if you have downloaded and backed up the installer of the game you bought on GoG then for all intents and purposes you own this game. It does not matter what GoG does from this point on. You will always be able to use it.
The license key you entered and the following offline check when installing from CD/disk was/is considered something entirely different.
I'd argue that the only reason that games today skip the license-check has absolutely nothing to do with DRM but with it being out of fashion and not considered to fulfilling its purpose anymore.
There was never a time when the definition of DRM didn't include license key checks.
All in all, the experience from GOG is much more customer friendly than other game stores (there are only a few other tiny stores that I know about that are DRM-free and don't require their client to be able to buy and/or download games). They aren't perfect but you can download the installer directly from the website if you want or use a client if you want. Games work fully offline with no code needed. You can refund a game for essentially any reason within 30 days even if you have downloaded and played the game (there is some unspecified limit to number of refunds but it isn't tiny if you are just refunding a few you don't like). I'm not 100% certain but I'm fairly sure they don't ever remove inactive accounts.
Unfortunately, the value of DRM-free is often reduced somewhat by the "release a buggy mess and if it sells well enough fix it eventually" philosophy that most developers have these days. Not having access to updates can worst case make the game unplayable and often makes it less pleasant (of course, there are also cases where updates make it worse :/). So DRM-free isn't a complete solution for not being able to access an account, but at least once you have played a game you can play the same version again even if you can't access your account.
While to some degree that is technically true but it is not what the whole DRM debate has been about.
Also, I think the DRM people are referring to here is the kind that consists of rootkits, monitoring software and similar or, in simple cases, refuses to run or gives you some kind of penalty when it detects certain other software.
I don’t expect any guarantees from digital goods being stored for free in a digital warehouse, unfortunately many do. One doesn’t own the nebulous copy on the distributor’s server, they own whatever copies they downloaded.
From that point on, even if you get banned you can still use your local installer copy.
I’m not sure if an offline-only key check would be considered DRM; maybe is. Realistically such a check doesn’t do much, so what’s the point in including it. Back in the day it was often required to have one of the discs inserted to play—that is definitely DRM.