Yes, they're a thing - in Port Lincoln, Australia, as part of the annual Tunarama festival. The 2018 championships have just been held there. The Telegraph reports:
Historically a fishing town, the idea grew from watching dock workers hurl fish from the decks of overflowing boats.
Dead fish were thrown in earlier editions of the event, first held in 1979, but the decision was made several years ago to toss rubber ones instead.
There's more at the link.
Here's some footage from last week's competition.
I suppose the losers were weighed in the scales and found wanting . . .