Can debut record a game from my PC?

Debut is intended to capture movement on a regular windows desktop. 3D fullscreen games run seperately from the regular windows Desktop, so attempting to use Debut for 3D capture may not have desirable outcomes.

The best way to find out though would be to try it.

Use avi, mpeg4 (native), with mp3 sound and you should get a decent framerate. Though this will depend on how fast your computer is and how intensive the game is.
If you're playing a game which is stressing your computer, you will likely get a 10-15 fps screen capture.

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