No, I would not consider any chess program to be an example
of an application in AI. Most, if not all, chess programs
are just brute force algorithms, combined with extensive
libraries for the opening game. After the opening, they just
explore all possible plies (a ply is a half-move) to a certain
depth, evaluate the postions, and prune to select the best moves
so far. Then they repeat the process of "try all, evaluate, prune
to select best so far" zero or more times.
This doesn't even come close to how a human chess player works.
Not much is know how exactly a human chess mind works, but
(grand)masters only explore a few moves in depth when its their
turn to move.
As for the learning process of Deep Blue, the only ones that
are "learning" are the programmers.