You'd probably be best using the xbox one itself as it's probably the most powerful stuff you could put in its formfactor. For an even smaller more powerful gaming system try a ps4 trolololololAny PC cases that size?? Bare, not already built systems.
Maybe something like the Silverstone ML06B http://www.silverstonetek.com/product.php?pid=457
I know they do a few cases that size and it's nearly the same size as an Xbox One