You can always play a game in windowed mode and just drop the window to eye level and leave the rest of the screen blank (or do like I do and use the spare real estate to leave an email client or youtube video running).
If you can rotate the monitor, you can play in "portrait" mode.
Technically that's what I'm doing with my NVSurround 3 monitor setup (all three monitors are in portrait mode, then fused together).