The Ether you are paying in that transaction is just the gas fee required for it to be accepted by the blockchain. It is given the the miners of the network and none if it is given to ether shrimp/croc. The hope of playing this game is that eventually you will be making more Ether than the fee is. That is when you will start making money.
If you want, you can choose how much you want to pay for the gas price in Metamask. But, if you lower it too much, it may take a long time to be processed or may never be processed by the blockchain.
That’s not accurate either because there are upper limits. Therefore, you and everyone else that is saying “play for free” is lying to the potential community. It’s not free if you can’t do anything; and you cannot do anything without at least a tiny bit of ETH. Even if the amount is negligible, it’s still more than zero and, therefore, not FREE.