It is difficult to type a lot of these TV personalities with any confidence because they tend to have very calculated public personas. As for Jon Stewart, I am confident that he is a Ti/Fe user. His cheeks are very flat throughout the entire interview (except for when he smiles), and his smiles do not clash with his cheeks. I am not very sure about his perception functions. I am leaning towards Si/Ne, if only because of the way his brows slant downwards from the center. His eyes look a bit too soft for Ni/Se eyes, but I've been fooled before and the quality of the video isn't great. He appears to be a Pi-lead; I noticed a handful of eye drifts throughout that interview. So, I guess I see him as an SiFe, but I am really not sure. I will have to pay more attention to his eyes the next time I watch his show.
I'm fairly certain he's an NT-Gamma. He zones out over to the right as he speaks in the Ni way and then sharply returns, and his smile at the very end looks Te>Fi to me. His speech pattern and tone of voice reminds me a lot of Robert Downey Jr. in the TeNi Larin video, and I know a lot of NiTe and TeNi that act and talk like him. There are things he says that seem very Te to me, like the "something you will never understand" parts. It's pretty common for Gammas, NiTe and TeNi in particular, to say things that seem really harsh or mean when they really don't mean it as strong or insulting, just true, and things like that are the most common offenders.
I couldn't say for my money which one I think he is. Either TeNi with high-Ni or NiTe with high-Te.
I have watched some more interviews with him, and I am now confident that he is an NiFe. His eyes look very Ni and zone out often. His eye drifts regularly cause his head to drift to the side in a manner that looks involuntary (Pi-lead). He displays very noticeable definition and use of his zygomaticus major muscle (located around the corners of his mouth, below the cheeks). Fe warmth (and sometimes Fe aggression) is strongly present in his mannerisms (gesticulations, browraises, etc.) and speech.
Sidenote: A lower-Fi smile rises up to the cheeks around the cheekbone area, but does not "break" the cheeks. Instead, it is "squeezed" by the cheeks. This results in a smile that is narrow and/or asymmetrical. A higher-Fi smile rises up to the cheeks around the bottom of the cheekbones, clashing with the cheeks but also "breaking" them to a degree. This results in a broader smile, similar to an Fe-smile, but with strong Fi tension in the cheeks. An Fe-smile rises diagonally up the side of the face, bypassing the cheeks altogether. The engagement of the zygomaticus major muscle causes the muscles around the cheeks to stretch. A tightening sensation can be seen around the cheeks, but there is no tension within the cheeks. While Jon Stewart's (and many other Fe-users') smile has the shape of a lot of subpolar-Fi users' smiles, it cannot be a subpolar-Fi smile because it does not clash with the cheeks. It bypasses them, and rises up the sides of his face towards the outer corners of his eyes.