Because their labor can be very cheaply duplicated by broadcasting the game to millions of spectators.

*> Where's the money actually coming from?

Ads, merchandising, and ticket sales, like you note.

Professional sports players are, economically, in the same category as musicians and actors. They produce media and the digital era means media can be duplicated at virtually no cost, so the value of their labor can be easily multiplied by a very large constant.

Police, doctors, and teachers provide their labor to individual humans in realspace which is much harder to scale so, unfortunately, their salaries reflect that.