Click on level 1.
I know I didn’t mention say it explicitly in my comment initially, but it was in my attempts to click on the first level (which resulted in nothing happening) that made me make the comment in the first place. I only had functionality with the Back button, none of the numbered level buttons were selectable at all. I’ve posted a screenshot of how it looked for me.
I did mess around, however, and it turns out to have just been something on my end! Turns out the Google Chrome add-on Privacy Badger had blocked the scripts that let me play levels in your game.