What isn't talked much about in this is that there are also restrictions when it comes to video game providers (digital distribution services, multiplayer services, etc.) From what I can tell, yes, you do have to provide an ID to purchase video games online. Many people already use their real credit/debit cards for Steam, Xbox Live, etc so it might not be a deal for some, but it is for those who use pre-paid cards and cryptocurrencies to purchase games.
From what I can tell, most multiplayer games are fine as long as they don't create some searchable profile about their users. If you run some community server for an online game, or a tunneling service for LAN games like XLink Kai, or some reverse engineered service for a defunct console's online functionality, you should be fine, from what I can tell.