Sysadmin

So you own zero books. Yeah? O'Reilly can barge into your house and take them back, because 'that's how copyright works.'

Or maybe that's not how anything works, despite every new form of popular media trying it for a while before being told they're not special.

No, copyleft licenses work differently. In particular, the thing that makes them valid (in contrast to EULAs, which are not) is that they actually offer consideration to the licensee.

Take the GPL v2 (which I mention because I'm most familiar with it) as an example:

Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program).

What it's doing there is affirming the user's ownership -- not mere "licensure" -- of his own copy. It's pointing out, in contrast to the lie of EULAs, that the licensor doesn't have any right to restrict the copy owner's property rights. In other words, you don't have to "accept the GPL" in order to use GPL software that somebody gives you; the license only kicks in if you want to do something with it that copyright law itself otherwise prohibits, namely, distributing copies or publishing modifications.

What EULA writers think they rely on -- and what they've managed to bamboozle some, but not all, courts into accepting -- is the notion that because computer programs require copying into RAM (if not also installation into a hard drive) to use, that that incidental act of copying somehow entitles publishers to impose additional restrictions in "consideration" for the mere use of the copy the user already bought. In reality, however, there's an explicit carve-out in 17 U.S. Code § 117 (a) (1) that pulls the rug out of that argument and renders most shrinkwrap and clickwrap EULAs total bunk because the owner already has the right to use his property and there is therefore no consideration. (Admittedly, Steam might be an exception to this, since Valve could try to argue that keeping track of your games for you and making them available to re-download whenever you want is "valuable consideration" -- but that's the exception, not the rule.)

(Also note that there are other problems with the validity of EULAs, such as the fact that they're contracts of adhesion, but I'm tired of writing so I'll leave that for another time.)

TL;DR: Copyleft licenses are valid because they offer the copy owner privileges they didn't already have: namely, permission to distribute copies under certain conditions. In contrast, EULAs are bunk because they attempt to restrict mere use of the thing the copy owner already owns while offering nothing in return.

Nobody thinks buying GTA V means you own the GTA franchise. Literally nobody. Not one soul.

But you own that copy. You own "the game," as surely as you own any other published work.

You're confusing copyright law with property law. Sure, you can't make and sell copies (fun fact: you can make copies for certain other purposes, though), but that's not a limitation on what you can do with your own copy, which is your property.

Ownership of the right to copy and ownership of the copy itself are entirely different things.