Soon, GOG and all other storefronts will state that you're purchasing a temporary digital license for any game who's publisher uses an EULA that states you don't own the game. This is due to the recently signed California law that forces storefronts to be transparent about the publishers EULA.
But also with GOG you can download the installers and play offline. It's literally one of their big selling points. It's less convenient than things like steam, but you can do whatever the hell you want when you buy it. So in that regard, it literally is a purchase. Or as close as you can get with digital goods.
Same thing applies to Steam. You don't need to use the Steam DRM if you don't want to, it gets added by the developers/publishers. There are plenty of DRM-free games on Steam
On a legal level, it is how GOG works. They still only sell licenses. You just have the loophole that their installers and the games installed by them will work regardless.
While that may be partly true, (also likely) depending on the county you're located, they're not able to revoke the license though.
The same is true for Steam, laws are laws
So in this specific case you having the files makes a world of difference.
You also have the files if you downloaded them on Steam. What's important is whether those files can be used on their own or if they're protected by some form of DRM. If the files can be used on their own it doesn't matter if you got them from Steam, GoG or a physical disc. If on the other hand the files are DRM protected you having them is useless, whoever controls the DRM controls your files, again regardless of where you got the files from.
Legally, it's still a license, it's just effectively impossible to revoke.
Edit to expand on this: A truly offline forever-purchase of physical goods can be re-sold. See https://en.wikipedia.org/wiki/First-sale_doctrine (this is the US-specific version, other jurisdictions may have similar doctrines).
American legal concept that limits the rights of an intellectual property owner to control resale of products embodying its intellectual property.
A digital "purchase" is usually non-transferable, even from GOG. It can't be removed from your own HDD once you download the installer, but there are still restrictions attached on what you can do with it, even if those are limited and hard to enforce.
Technically, probably yes, but you can buy old, opened games on eBay. I doubt you can do the same with GOG games. Digital media is much harder if not impossible to resell.
A small minority of GOG games have DRM, a majority of Steam games have a form of DRM. "Use a simulator" isn't a solution, I shouldn't need a third party program to play the games I paid for.
Also there's a pretty big difference between downloading the installer and backing up the installed files, one is an intended backup solution, the other is a workaround.
Which gog games have DRM? The costumers over there even protested Hitman's inclusion in the store precisely because without internet you can't unlock anything in the game, GOG even removed it from sale.