Set the content type to video/mov and that is evidently not set up in TW core. So I tried video/mp4 and now the video plays just fine, but with no audio! 
I’m guessing I will need to convert the videos to mp4, but just thought I would throw out a question as to whether or not .mov files can be played? This is a local file which will be copied to the server but never embedded as a binary.
Browser support is the core issue I believe in most cases.
I have used mp4 successfully with Tiddlywiki5 and Mozilla, Chrome etc.
HOWEVER if you are using TiddlyDesktop(1) then mp4 will be an issue - I use webm (2) now as a result, I use ffmpeg on the command line to transcode to webm. I actually have a tiddler in my wiki with these incantations because I find I am always needing them and can never recall the syntax.
TiddlyDesktop uses headless chrome - there are royalty issues with mp4 hence lack of codecs/support.
For anyone wanting to convert to webm using ffmpeg here is a starting point - in this case converting mkv to webm but mp4 would be the same - this is my standard incantation for preparing TiddlyDesktop videos ( webm with vp9 codec ).
ffmpeg -i myVideo.mkv -c:v libvpx-vp9 -b:v 512k myVideo.webm
Others may correct what I have said which is all based on memory - I guess with these sorts of things once we have a formula that works for us we rarely revisit the topic and so the advice tends to be a bit “historic” 
Update: webm is supposed to be marginally better than mp4 in terms of compression, when transcoding I try by means of trial and error to hit very roughly the same file size as the original mp4 file by altering the bit rate - shown as 512k in the example - a video expert would probably shudder at this crude ‘guesstimation’ but it works out in practise for me.
Makes sense!
I typically save things like this on github gists, in part so they are public/searchable. Can you talk more about how you store these? Separate tiddlers?
Using TW Desktop 0.0.14 (15) with local .mp4 video displayed with <<videoplay "path to file.mp4" "displayed name">> works fine on macos here.
Good to know, but give that this will also need to be playable from a web page online, I’m going to try the webm path first…
Note if I remember correctly mkv gave me a video output in TiddlyDesktop- the issue there was the same as yours - no audio - the notes I made at the time suggested that the audio codec was the problem there AC3 - licensing issue? Either way moving over to webm so far has been problem free for me other than of course the hassle of transcoding them.
So this is a file linked to from a single file wiki? And how will it be served online - through a web server like nginx? I feel like the latter question would make the biggest difference because the web server is basically telling the browser what kind of file it is.
Single-file html TW > GitHub > Netlify - served as plain html.