Every time any tournament player enters an otb rated tournament they play for money.
I enter tourneys to play serious chess, play new people and hopefully improve my rating. If i win money, that's a bonus, but I never enter expecting to win any money.
I never go into a tournament with the goal of winning money. If it happens then fine, but its not my goal. I go into tournaments looking to have fun, see old friends, make new friends, see new places, visit familiar places.
I took the OP much differently, such as playing with the primary goal to win money.
I've also played in low entry, no prize or trophies only, events. Those are not as common though.
Did you ever play chess for money...?? Just like poker or blackjack but than in chess..