"... Very well. I see your point. I will call this Dr. Stein."
"By 'this Dr. Stein,' do I take it you never met him?"
"That's correct. I've a vague recollection of speaking
  to him once on the telephone."

(Jeremiah Healy. 1984. Blunt Darts. New York: Pocket Books. P. 24.)

 

Intuitively, the contrast between this and that seems parallel to the difference between here and there, but notice the difference between these two utterances:

(1) How about that Putin!

(2) How about this Putin!

If the speaker and the listener are watching television together, How about that Putin! is appropriate, but not How about this Putin! However, if the listener is in the next room and not watching, or if the speaker is reading about Putin in the newspaper, then How about this Putin! is possible. This excludes the listener, and is not likely to be uttered if both speaker and listener are sitting next to each other in front of the television. How about that Putin! is possible in those contexts, where the speaker and listener are both watching the television and also where only the speaker is watching (or where the speaker is reading the paper), How about that Putin! suggests a sense of shared experience/attitude and/or comeraderie.

Uttered by an ENT, the choice of that in

(3) How's that throat?

suggests a previous visit (the shared experience) as well as sympathy/concern on the part of the physician. The use of this suggests that the item has not yet been discussed:

(4) How's this throat?

In saying How's this throat?, the ENT is disclosing for the first time his interest in the patient's throat. He is palpating it for the first time, while How's that throat? suggests a second visit to the doctor.

If that suggests comeraderie, what do we know about this that allows us to guess that the speaker has not met Dr. Stein?