I've been waiting years (almost) for Shadow Complex to be ported to the PC or the iPad. Can I somehow play Xbox arcade games on my PC?
Sadly, no. Xbox Live Arcade games cannot be played on a PC. You'll have to wait for a release on another platform in order to play on that platform.
The Xbox 360's architecture is significantly different from the PC's, although Microsoft offers certain cross-platform SDK's to ease portability between the two.