You can look at it both ways. For example, suppose you bet $11 to win $10 on a game.
Loser pays: One could say it is an even-money bet, with a $1 refundable fee if you win. So, only the losers end up paying the fee.
Winner pays: A fair even-money bet would win $11 for an $11 bet. However, if the bet wins, the winner gets only $10. The missing dollar could be viewed as a commission or fee.
Personally, I view it as both pay in the form of a 4.54% house edge, assuming a 50% probability of winning.