"But, my dear friend, put yourself in my place,” replied the Musketeer. “I was hipped to death;

I think it is obvious that "hipped" refers to being thrown in a wrestling match. Here is refers to an emotional state
after an unpleasant experience.

hipped 2
adj.
5< HYP(OCHONDRIA)6
1 [Now Rare] melancholy or depressed
>2 [Colloq.] having a great, often excessive, interest; obsessed: with on !hipped on movies"

If it wasn't for the Muskateer citation my first reaction to hipped would have been that he had been so inundated with hipness and hip things, and the need to be hip, that he had bee "hipped to death", in a manner of speaking. Based on this definition of "hip".

>Main Entry: 4hip
Function: adjective
Inflected Form(s): hip·per; hip·pest
Etymology: alteration of 2hep
Date: 1904
: characterized by a keen informed awareness of or involvement in the newest developments or styles <