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

The name or symbol of the tokens may be the same. and they can also list on certain exchanges. But, the smart contracts will be always different, there will not be the same smart contract in which we can check them. That is why it is better to put your smart contract on your website or other information channels.
So far there are many fake tokens that we can find especially in the new exchanges or not reputable exchanges. that's why before buying any tokens it is better to check them on their group officially to ensure the smart contract and also check on the coin market cap.