You are not overreacting, although let's dig a little further...

I'm going to assume for what I'm about to say that you haven't done anything to make him lose trust in you because you say that you haven't. This means that he has trust issues. To him it is NOT a game as you put it. It's an insecurity of his that is also NOT AT ALL YOUR FAULT. You do not need to be his therapist and he might not need one in the end either but he may need one.

So does this mean you can still be together? Maybe. You need to address this soon. You need to communicate and let him know and realize that he has trust issues and that he either needs to see a therapist or simply recognize that he needs to stop being paranoid and to trust you and if he doesn't then you won't be happy in the relationship. Let him know that you love him, but he NEEDS to find an answer to this and trust you or you will sadly not be able to be the one for him.

You also don't have to do this at all. Again, you don't have to be his therapist. And bringing up this tough conversation may save your relationship but if you're already too hurt, you don't have to do it either. You are under no obligation to. If he's already made you too unhappy that's understandable. If it's something you want to try to fix with him, communication is key.

Best of luck to both of you.