'That' in 'that is why' is a demonstrative pronoun. 'That' as a relative pronoun isn't preceded by a comma. Interestingly, 'which is why' is similar to 'that is why', but it functions as a relative pronoun.
I agree with Ahmed on all counts. "That is why" should be preceded by a period, a semicolon, a colon, an em dash, or a linker, that is, something that sets it off as a separate sentence. Only "which is why" can be preceded by a comma as it introduces a sentential relative clause.
I would hyphenate the compound adjectives. I also find the "the men who do it are aware of it" part defective, so the sentence as a whole should be recast:
- Boxing is a high-risk, short-term career, and the men who practice it are aware of this. That is why they are paid so highly. (This is actually ambiguous — it sounds like they are paid highly because they are aware of the high risk and the short-livedness of the activity.)
Better: Boxing is a high-risk, short-term career. That is why the men who practice it are paid so highly.
Option with "which": Boxing is a high-risk, short-term career, which is why the men who practice it are paid so highly.