Some Web API only works well on a certain browser despite it’s implemented in most of majority browsers. In case I accidentally use experimental API that only works well in Chrome. Can I make my game only available in Chrome and reject other browsers?

You can, but remember that you'd like to have your game played (and voted on) by as many devs as possible - if many of them will see a broken page under, for example, Firefox, they will either skip it entirely or give you a one-star rating. If you're ok with that, then go for it.