There's a encoding setup for mp4 that is designed for streaming, and it's not necessarily set up that way by default. So it may be that it isn't set to be streamed, but chrome is addressing that right and Firefox isn't, for whatever reason.
I switched to mkv ages ago and haven't used Handbrake in a decade, and I can't remember the specifics for mp4 settings or features, and I'm not gonna download and analyze that file. But if your encoder has a web setting and you intend for the file to be streamed over the web, use the web setting.
I downloaded it before watching it.