Just to be super clear, the rest of Hypnospace appears to work fine, just the Outlaw "game-within-a-game" does not respond to button prompts?
With C-Robin the issue turned out to be that there were multiple controllers plugged in and the game got confused where input was coming from. Try disconnecting all controllers other than the one you want to play with, including wireless and wired controllers (and dongles). If it still does not work try removing all other USB devices and try again. Please restart your Xbox and try again if any of the above does not work the first try :)