No, tying knots isn't an application of knot theory. To learn about some applications of knot theory, you could read the textbook in the OP.
Neck ties are a mathematical knot if you again assume the two ends are connected. See other comment in this thread.
Knot theory here only determines the "shapes" of the knots and which are "allowed", there is no friction, width, etc.
https://en.m.wikipedia.org/wiki/Link_(knot_theory)
https://math.stackexchange.com/questions/217670/is-there-a-m...