Sorry I didn't respond on this sooner, but I have never worked on trying to do push notifications from PHP before. This is a very interesting solution, though!
Hmmm....first and foremost it really sounds like a mobile app idea. Anything related to push notifications really shines on mobile where a system to display notifications at any time exists. A web interface could tie-in as well, but it really sounds like a mobile play.
I will say that perhaps PHP is not the best-equipped for this. Node.js may be a better direction. Node is more flexible than PHP when it comes to push notifications, REST web services (probably the best way to communicate with mobile apps) are dead-simple, and possibly most important is that node works very well when it comes to being reactive to data. What I mean by that is when a notification comes into your system from one of the data sources (forums, games, etc.), you can easily spark-up the system to do what you need to do. It would be a bit more complicated in PHP, and may require command-line PHP scripts depending on how the data reaches you (web service requests could start-up a PHP application since they can be viewed as regular HTTP requests, but socket connections are more complicated in PHP than in node). Plus, your whole system for push notifications can be folded into your application, rather than depending on a third-party push service. Node excels at all kinds of socket communications.