I don’t know that a screensaver will run on top of a game. You could definitely try setting it to a minute, load up your game and leave it idle to check, or try setting the display to sleep after a minute in the power management options and see if that works.
Does your TV have a shutdown after X amount of inactivity option? My Sony can be set to shut down after 1, 2, or 4 hours of not receiving any input from the remote. (Changing volume etc.) It will put up a prompt for a few minutes and turn off if you don’t press anything on the remote. The annoying thing, is that I would prefer 3 hours. 2 can still show up during a particularly long film, and 4 is longer than I need.
Failing that, it probably has the old “sleep timer” option.
And if you don't have that option, you can probably create a batch file on your PC, and run it with a keyboard shortcut:
shutdown -s -f -t 5400
This should abort any current shutdown process, and set a new timer to shut down your PC after 90 minutes. (run shutdown -?
in a command prompt If you want more options)