Looking at the video clips, and considering his theories, Jung seems to be very comfortable with using inductive reasoning to draw abstract conclusions.
INTPs seem rather uncomfortable with inductive leaps. INTPs seem to often get stuck on the details of the deductive process, and when the deductive process stalls (for lack of proof), have a hard time making an inductive leap to push beyond the reach of deduction.
It depends on the INTP. You're talking about N-heavy INTPs versus T-heavy INTPs. I know I've flipped back and forth lots of times in my life between those modes of approach.
Once you get a framework and baseline established with Ti+Ne, that framework suggests all the other elements of the model. (Basically, "if this, this, and this are true, then this must be true as well.")
So Jung can basically be operating from a Ti+Ne perspective IF he has firmly tested and established the basics of his model to his logic's satisfaction. If his assumptions are true, then his speculations can also be deemed trustworthy because they follow rationally -- thus he uses Ti to speak with conviction.
You can also intuit backwards, through the N sense rather than the T. Basically, if you nail enough points onto the board in the proper relationship to each other, you can go by 'relational logic' to nail in other points... very much like an FBI database scanning millions of faces can use certain pivotal points on a face to hone in on the target visage. it's not needing to logic-crunch everything, it's just comparing relational distances and "big picture recognition" against other images on file, and you can "fill in the gaps" so to speak and conclude what must be there.... an N approach. The difference between Ne+Ti (ENTP) vs Ti+Ne (INTP) in this regard is that the INTP operating via Ne+Ti is still working to create and conform to a model, while ENTP even if using a Ti+Ne process is less about the model and more about exploring possibilities.
Why do people feel his thinking function is Ti rather than Te?
See above.
You should debate religious and/or philosophical theory with a Te person and then a Ti person, and you'll see a difference between who focuses on constructive a conceptual argument that can operate purely in conceptual terms (sort of like the logical arguments constructed in the Mathematics Logic course in collegiate settings) versus an argument that depends on particular data points from which broad conclusions are drawn. Arguments with Te tend to be proactive tools to help accomplish the person's goal, Ti arguments tend to be diffuse, not applied easily in a practical way, they exist for their own merit.
... sorry, lots of "sketching" mentally here, i'm not sure if I painted a clear picture even to myself.
EDIT: Was thinking more about IxTJ versus IxTP. I think to say it more clearly, IxTJ is about using Te to support and implement the perception. The perception is not in doubt; the INTJ chooses the perception that is useful/appealing/sensible to them, the ISTJ sees the core perception (what the object is "supposed" to be), but they both use Te to then implement and support it. The perception is already there, an image and thus an ideal to be realized.
The IxTP uses Pe to support the Ti judgment. Judging functions take in and "crunch" data. Thus the quality of Ti is based on the data being crunched, and the conclusion (or ideal image) is not an Ni/Si image that just exists, it's a natural conclusion of the Ti process fueled by Pe.
So logic is being used in two different ways here. Logic naturally creates the conclusion for Ti people, logic is used to buttress the perception in Te people.