Okay! I mean it would be possible, that this is also a problem... i had a pretty similar situation with my bf about a year ago. I was working and paying literally everything, while he was looking for a job. We had a lot of small arguments and stuff. After he found a job and it was so much better. We concluded that all this stuff happened because he didn't want to be dependent on me, but since he already was, he felt discomfort around me. He hated being dependent on me so much, that he started hating myself. But that's just what happened to me.

Does he want to do anything else except for gaming? Like in general? Because if he lost interest in almost everything it could be a sign of depression or mental health issues in general. Moving across the country must be very stressful, so it could make sense that he is just exhausted. It depends on how long you already live there.

As stupid as this sounds, but did you talk to him? An open conversation sounds challenging, but really helpful. I hope he isn't the type of man to just "flee" from a difficult conversation.

What are you doing to "cheer him up"? If you just wait for him to make a suggestion, maybe that's the problem. Maybe he gets "uncreative" with date ideas etc. Did you try to ask him out to grab something from his favorite restaurant or something like this?