This might be a change in Chrome.
From what I recall, when I would click on the play button from the finished recordings page, it saved a file in my downloads with a ".m3u" extension. Chrome would then launch VLC to play the file. But now, it appears that Chrome thinks it can play the video with an internal video player as it brings up something that looks like a video player... that doesn't play anything.
I haven't been able to find any way to prevent Chrome from attempting to play the video.
It's also possible the content type header that the tvheadend server is sending in the response has changed, or is causing this problem.
Having said that, if I right click the play button and select "open in new (window/tab)" and then right click in that new window/tab I can select "save as". that results in the ".mu3" file being saved. I can then open the saved file and it plays in vlc as expected.