“Paid by their sponsors”??
That’s correct, if what you mean is the sponsors for a tournament. PGA tournaments from the least to the top have one or more corporate sponsors of the tournament and many major tournaments are also sponsoring a charity as well.
And players who qualify for and play in a tournament are paid according to how their final score in the tournament ranked:
Sponsors of PGA tournaments pay on the supposition that it is good advertising for their company, and good public relations as well when the tournaments is also donating to a charity.
Right. And pro athletes are pretty much always paid by sponsors, even if a team or other organization is the intermediary. Nothing special or elevated about the Ryder Cup.