1. To thoroughly trounce someone in a game; similar to pwn, pwned, or its variants. Can be used as a verb, adverb, adjective, etc, in a similar way.
2. To literally stomp a kitten, usually to death, usually in the context of sadomasochistic fetishes. Similar in spirit to seal clubbing.
*A gets B in the back with an energy sword*
A: damn dude, I just kittenstomped you so hard.
A: Oh my god, what are you watching?
B: This woman kittenstomping that cat.
A: ...dude, what are /you/ doing?
B: ...what? Oh, nothing...