have you tried putting the shortcut to the game on the monitor you want to use and run it from there. seems to me that stuff opens on the screen the shortcut is on at the time, though i have never tried it with a game.
second thought is to run the game in windowed mode once and then move it to the right screen. it usually remembers the last screen it was on and restarts there. MPC runs that way for me. i use it on the 3rd screen (a tv i use for watching video) and it opens on that screen when i open a video file once i moved it to that screen a few times.
just a couple thoughts i had after thinking about it for a bit while working.