How to finance gas-fees for my own alt-coin?

When you develop a custom token that mines tokens depending on some actions, each transaction to let users gain tokens costs gas-fees. A good example is a "crypto game" where you will receive in-app currency that is basically a cryptocurrency.

So if I deploy my own token to the ETH blockchain for example, how to pay for the gas-fees? I basically have a shitcoin that is worth nothing, who pays for the transactions? I guess always the user, but how is this even possible?

What am I missing here? Should I provide own nodes that mine the transactions?