Sooner or later I will use that. By now, I don't want to learn all that new stuff.
I'm not using JSP/Servlets but my own server via sockets and there is already the stuff for simple multiplayer games and user management implemented.
Ok. If you're running your own socket server, then some re-work would certainly be required. I had visited your site, and it was not obvious to me that it was backed by anything like that.
The only simple example for Java for Google App Engine I could find was a guestbook via Servlets, not very interesting for me. I will wait some more time and decide later if Google could suit my needs (I don't want to just store scores).
LOL. We're certainly capable of doing more than storing your high scores.
The kinds of changes you'd need to port to App Engine would be adapting your client-server protocol to run over http. Instead of starting up your own single server process, you'd create a servlet entry-point that could serve your client requests. App Engine would automatically spin it up on as many JVMs as would be needed to keep up with your clients.
App Engine is designed to make applications transparently scale, and we can't do that for you if you do things like directly listen on sockets, etc...
Let me know if you change your mind and have any questions.