Selling your game would be "inuse" trademarking, therefore a screenshot should be enough.
Probably not, no.
Most companies -- at least, those with any amount of resources -- will pay the small trademark filing fee and get the registered trademark.
To challenge that mark requires far more than a screenshot. It requires demonstrating that the mark was used in commerce before that data, and depending on how much advertising the other company has been doing, probably would require that the earlier product demonstrate that the mark actually has picked up secondary value associated with the company or the product.
It wouldn't be enough to say "Here is a screenshot of Rich's Game, with the game title Rich's Game". You'd have to show the title "Rich's Game" was released before the earlier date, and if the other company had the forethought to register the intent to use the mark, you would have to show that people actually know about the title "Rich's Game", and at least some people -- customers or active players I imagine -- already knew about the product by that name before the other company sent in their registration.
If it wasn't worth the $225 filing fee, it probably isn't worth the much higher cost of protecting the name through legal channels. It is probably easier to pick a different name.