When they say "no play offs", they mean, you don't get a second chance if you lose.
(The terminology here is not conventional American English, but from the reference to Wimbledon the writer is probably British, so maybe this is the terminology in British English.)
Anyway, the way such a contest works is this. Say we have 8 contestants. We pair them off into 4 contests. In each contest one person wins and one person loses. The losers are then eliminated from the tournament. That leaves 4 winners. Now we break the 4 winners into 2 contests. That gives 2 losers and 2 winners. The 2 winners then compete for the championship. One wins and one loses. The winner is declared the winner of the tournament.
So "no play offs" means that once you lose a game, you're out. You don't get to play another game. If the second best player has the bad luck to be paired against the best player in the first round, he'll be eliminated in the first round. The final round is not necessarily between the 2 best players. Who ends up in second place depends on who they got paired against.