This game is pretty awesome! It didn't start for me in Firefox, but works fine in Chromium.
Thanks!
It still didn't work, so I had a closer look and found this in the console:
"Request to access cookie or storage on “https://v6p9d9t4.ssl.hwcdn.net/html/1160227-123780/index.html” was blocked because we are blocking all third-party storage access requests and content blocking is enabled."
Turns out this happened due to my privacy settings:
Cookies and Site Data -> Block Cookies and Site Data -> All third-party cookies
I added "https://itch.io" to the exceptions and now it works. It's important to prefix with "https://", just "itch.io" won't work.