I was wondering the same thing last night when i was watching the beginning of the millionaire show. If he is an INTP then he's a remarkable actor. Extroverted, likely sensing, borderline f/t, probably J and without a doubt annoying as hell.
Lots of Ti game show hosts try to act more friendly and extroverted on their shows, which is why Regis might seem more ExFx for the camera (assuming I'm right about him, which I'm probably not because I've only seen Regis a handful of times, and I don't know anything about him personally).
Then you've got other INTP game show hosts like Alex Trebek who don't give a flipping shit if they come off as cold and aloof.
My intuition tells me that Philbin is bottling up some kind of anger, "Regis Rage" if you will, and that he would probably beat up people in parking lots if he couldn't channel said rage through his semi-aggressive shtick.
Other than that, I have no insight on what type he might be. All I know is that he scares me sometimes.
"Nobody in life gets exactly what they thought they were going to get, but if you work really hard, and you're kind, amazing things will happen. I'm telling you...amazing things will happen" --Conan O'Brien