You are buying a copy though, and would be expected to have the right to resell it. So digital stores go out of their way to "license" the copyrighted work instead of selling you a copy.

I have been thinking about this lately, and figured that another difference with classic media was the "live service" model, where games receive updates.

You can't take for granted that a copy comes with updates, so I guess that as a middle ground, publishers could license updates (and online multiplayer) & sell copies of the game. Sell your copy, fine, but if you want updates or multiplayer, you have to purchase a subscription again. This would make more sense to me, but may be difficult to communicate and implement.