Besides, pragmatism is relative. On top of that, House is only staunchly pragmatic once it becomes a REAL mystery. Up until that point, he incessantly launches games and competitions, often deliberately disrupting the order (a non Te, and way Ne thing to do) sometimes doing so for that exclusive exclusive purpose.
An ENTP who's got a half-way decent Thinking faculty will turn pragmatic once they see that the games are getting in the way, but will otherwise allow themselves to play.
This is an exact counter-example of what the INTJ does. Refusal to cooperate in any game (we see this a lot in Foreman, who is obviously an INTJ) until everything is taken care of and settled.
See the first episode where Foreman comes back after quitting in the new season. The one with the guy who steals personality.
Once the case is solved, Foreman has the idea for a game. House started off with them.