I think that's the fault of whatever app / frontend you are using. On OP's instance (which is just rendering HTML), and on the community's instance (using lemmy-ui), this file plays. In both cases, it's a bog-standard MP4 inside a VIDEO tag with a video/mp4 type. If - for example - you're using Sync, then that app also can't play MP4s hosted by Mastodon either.
In voyager the video plays if you click on the thread and view the video there. It doesn’t show the video if you just click from the main page. That gave me the error op had.
Checked with your instance (feddit.nl), community's instance (sh.itjust.works), and with lemmy.world. None show a thumbnail, but all can play the video (at least on default interface).
Indeed, for some reason, the video cannot be viewed when opened in another browser tab