The app is a digital pass. The counter is for the entry, so no pass is needed (you're essentially buying and redeeming the pass in the same transaction if done at the counter)
If you're actually shelling out $59 for a pass, I would suggest that you do it at the counter. If the club is full, they may turn away passholders, so if you purchased the digital pass in advance, you could be stuck with it if they don't let you in.