If both the XBOX and the RPTV instructions tell you to avoid playing video games on such TV sets ... don't you think they might be onto something?
Yes there is a danger, but if you keep the play time limited and the contrast low ... you can play for at least a short time. You also have to keep an eye out for the wrong kind of games ... those with plenty of static images.
Bear in mind if you damage the TV, this is not covered under warranty. It is called abuse.
Michael, as usual, is right. But if it were me, I'd never consider connecting a game console to an RPTV. You could do as Michael suggests, but there's always that danger. The thing is, avoid stationary image fields.
I think you'd be much better off by reserving your XBox for a direct-view set in the house. And even then, you have to take the same precautions as you would with an RPTV--keep that contrast low and avoid prolonged exposure to stationary image fields. (But direct-views can withstand this sort of treatment a little better than RPTVs.)