If I’m reading that image correctly, it looks like the ISP may be in Egypt? Telecom Egypt - We Space - Gaming Bundles.

That doesn’t change your question or the answer, but it’s interesting to note that Sony and Microsoft likely have formed agreements with TelecomEgypt to offer these plans. We could speculate about the details of what those private corp-to-corp agreements might look like, or whether we think it’s morally acceptable to do it; but regardless of all that it’s probably legal and it is part of the reality we live in.

As others have pointed out, when you are using a router provided by your ISP, the ISP can identify the devices on your network. If you choose to use your own router, the ISP still may be able to identify traffic that is directed towards particular gaming servers, although the ISP might choose to only honor the gaming bundle pricing if you use their router. I don’t know anything about the details, but it may be that Sony and Microsoft provide a list of destination addresses that identify which games are being played, making it easy for the ISP to identify those particular games when the ISP-owned router routes a request either to those servers or to other servers that aren’t covered by the gaming bundle. It’s also possible that the ISP may not even bother to try to understand which devices are using the network, and instead simply assume that requests routed to the listed destinations are covered by the bundle.