Let's assume i have created a game, and then created ERC tokens (Example swords) so the player must buy a token to be able to play the game.
What if someone creates similar tokens in his wallet and injects them into my game as if they are bought from my tokens store

This is the function of a smart contract, it can't forge your token. If someone creates a new coin with the same name, same decimal, even with the same code, they also cannot deposit to a platform with a different smart contract. Understand the meaning of smart contracts, so you don't have to ask about this anymore. There are many fake coins circulating in Ethereum smart contracts, BSC, but they can't have any effect on the official coins. It's just that they can fool people who don't understand smart contracts. If you want to deposit any coins, the first thing you need to look at is the smart contract, then the blockchain used. If different, do not do anything, because it will lose your assets.