Anyway, Smooth has the right idea. You run it like any coin/token distribution where all the coins start in the depository wallet.
How do players claim these coins in an automated way?
By withdrawing, the same as any other depository. Whether it is automated or not depends on how the depository is set up. If I recall correctly some operations (maybe only deposits?) were previously automated, some required manual assistance from the depository operator.
I'm talking about claiming the CK they'd be withdrawing? How would you automate the process so iluvbitcoins wouldn't have to manually check their M consumes?