House's "Moriarty" was supposed to be the man who shot him at the end of Season 2. (Though never given a name on-screen, that's the character was called Jack Moriarty in the script.)
Ah, yes. Forgot about that one. I guess, particularly because while he was a good foil for House in that episode, it didn't seem to be quite as "epic" as a confrontation between House and a Moriarty-style character should be. The most recent Holmes movie w/ Downy Jr. is a good example of how this should work, not to mention the various other such encounters that have happened in Holmes-based shows over the years.
This guy could have been an excellent adversary for House, had he been an ongoing character throughout the rest of the series. Hell, even Vogler and Tritter got more screen time that him.