No, you have it exactly right. I posit that a service run by a platform-holder who has a legitimate need to validate players' identity in this manner, for these reasons, is not quite the same as the video games (even the multiplayer ones) which have existed up until now. They have built something very different. And it's great! I just think it's also important to discuss what it really is, why, and the current+future implications.

I feel there should be a new term to describe this type of game. Up until now "eSports" has been used but that seems passe. Metagame perhaps? Might have sounded dumb a few years ago, but there's strong precedent now :P