Lyric discussion by losteyesight 

Cover art for Checkered Floor lyrics by Silversun Pickups

I also think of Chess as the other two postings have sugessted. Psychophants are like the pawns in the game if You think about it. Which by definition are those who attempts to curry favor by flattering influential people. (The King) or ("Our Star") lot's of other hints like "play along" and "while their backs were turned" could relate to chess when it comes to capturing the figurines as You play.