Notes:
This game runs very smoothly on Firefox, but on Chrome, I had to enable the experimental setting at chrome://flags/#enable-pointer-lock-options. I also had to click on the URL bar and hit F11 to get it to start capturing mouse input. After that it started working without fullscreen.
Hint: When you start a new game, hit the ~ button and type in +mlook to be able to look up and down with the mouse.