I made a pass at improving the webpage. You can check it out here: https://warpzone.itch.io/public-game-002
I've always been told to put the controls at the top of the page and the call-to-action first. But the controls should be in the game anyway, and the call-to-action only works if people already care about the game, which means they've already played it.
Making the animated gifs nearly killed me. The tools worked, they just made files that were too big for itch to allow me to upload them. So I settled on 3 seperate animated gifs with text headings between them explaining what you're looking at in the most hype way I could think of.