I was subscribed to Apple Arcade about two years ago, for a month. I guess I must have allowed it to send notifications back then. Or maybe I did allow Game Center to send them. Either way, I’m sure that it is technically perfectly fine for this push notification to be sent.
But as I’m currently not subscibed to Apple Arcade and haven’t had access to this game since my subscription ended two years ago, this is basically just a very personalized ad. And apparently an unintentional one at that: Unfortunately I didn’t have the foresight to start recording before I tapped it, but it just opened the App Store app. Not even on the Arcade page, just the default landing.