Some apps such as sky, bt sports etc don't let you screen share via HDMI due to rights restrictions apparently, I'd guess some games would be the same. Quality is pretty good though when it works
Goto the webpage and search for AirPlay support, or do a google search for (app name) airplay. If its not supported you'll usually find out pretty quick.
EDIT: I said AirPlay because they will likely block both not just one or the other.