YTA. The house is yours and you can charge as much as you want for rent regardless of the reason. But you have nothing to do with what he does with his money and if he needs to make any mistake that's something that he'll have to learn, your attitude doesn't help and also who said he will make such mistakes anyway?

You are being judgemental with his gaming habits. I realize gaming can be a problem but you are stepping out of your space and treating him like a child, and that can be more damaging to him in the long run because he'll may always think mommy will be around to make the right decisions and his ability to judge things in life can become impaired.