Why do top professional sport players get usually paid so much?
tl;dr There is a lot of demand for what they produce.

A proper answer should have some evidence, perhaps I will add that when I have more time.

Even within a category, say, football (soccer) players, you see a lot of discrimination: Top players at top clubs in top leagues get most of the cake. This is anecdotal evidence for the demand side story:


Only the best leagues earn much money through television rights, because only there is most of the demand (how much media coverage do you have for your national third league anyways?)
Only the best teams in these leagues get most of this money, mostly because leagues partly pay teams based on their performance ranking wise 
Only the best players get the highest share, which is a combination of the previous two facts, and that these guys are quite unique and have hence an even higher demand:

They make more marketing money (people really want to see them)


Due to their uniqueness, they can bargain better deals with teams and sponsors



Note that the last point is really the only supply-side story. If you ignore super stars, the supply of good players is huge. Most of the twist really comes from some of them being marginally better / lucky, making it into the better leagues, which happen to be the one that mass media demand, and get the high compensation.