Got it working in Chrome by enabling some experimental WebGL support. It still didn't work stable (sometimes it reacted to the keyboard, sometimes it did not, very strange!)
The game idea is very original. It's telling a story but also combining action sequences with a more common platform style. I like the visual effects.. as the fog on the main screen or seen through the window ... or that explosion animation shaking the whole frame. I liked the story and wished it was developing further... but well limited time... and maybe you had to learn a lot about how to work with Godot within that time (as I had to). Hope to see you again in some other Godot Wild Jams!
I had some issues myself with the HTML5 export, when directly let Godot package it as a ZIP file. I later chose normal export and then zipped it manually. That worked. I also got an error about "API mismatch" - so this might be the issue. Or you might want to try a different/stable Godot version (3.3.3). Hope that helps.