I don’t have a problem. It’s part of League revenue.
As to the integrity, I don’t see a problem. The League just gets a little for every bet placed, not when a particular team wins.
I think that this is the key to making it not fishy. This isn't the players being in a position to be on one side or another of a bet. That would be straight up crooked. This is the League skimming some money off the top of the profits of their gambling partners, and the players getting a cut of that.
The only way I can think that a player could affect that would be to make a play that puts a game in a more exciting position to increase in-game betting, which might then make next year's salary cap number infinitesimally higher than it would have been, and then if that player is a free agent next season, he might benefit from that.
Whatever theoretical benefit that hypothetical situation might be to a player is far outweighed by his incentive to just play well and get his FA money that way.