This is totally logical, but psychologically hard.

When I was a student I had totally-free online stuff I built lead to a stream of requests for upgrades, additions, bugfixes, etc. -- and the unreasonable ones are easy to discard, but some requests would be polite, friendly, and include offers to help. I'd agree to make the seemingly-small tweak, or accept the help, and then realize after a week that I didn't really have the time, or that my TO-DO list was being pulled completely out of whack....

Better to not publish your email address at all, perhaps, or make very clear that emails may be eventually read but very likely not responded to.

This is the correct answer. OP, you really shouldn't feel bad about not responding to people emailing you about a free-to-play game.

Besides, most of them are probably just writing to tell you how much they like it, or wanting you to partner with them.

You don't have to answer any of them. Just put up an autoresponder explaining that this is a free game and you're a university student and can't respond to email.

I mean, this is what Google does and many/most people love Google products.

Yep, or put up a paywall. Want to get answer to a question, pay $50/hour. Don't want to pay? Then deal with it. it's a FREE game.

Some people do care about the experience they provide, whether people are paying for it or not. Their pride in the game is important. They feel it reflects poorly on them if they're not providing good service. I can see how this would provide unwanted pressure when you're trying to study hard.