It appears that the server is listening into where the video is being served from and is blocking certain situations. When hosted on a server (not previewed from the local filesystem or localhost), it works correctly: https://tumult.com/support/temporary/2016/testvid.html
One workaround for this is to create a barebones HTML file containing a reference to that video on the same server. You can then load an HTML widget with that URL as your 'source URL' within Hype.
The headers from the file are showing that a 'playback session' is being set, and only the first byte is being sent when previewing locally. I got this output from Safari after attempting to load this video in a local preview. In short, the server is doing weird stuff when it doesn't detect that the video is embedded into something it recognizes as a 'website'.
curl 'http://www.pmbuy.ro/images/animatii/sexta.mp4' \
-H 'Referer: http://127.0.0.1:58608/preview/ABE4C308-C9F0-4313-B05F-41C5800CCBB2-610-00000A1C700ACC3B/index.html' \
-H 'Accept: */*' \
-H 'Connection: Keep-Alive' \
-H 'Accept-Encoding: identity' \
-H 'DNT: 1' \
-H 'Range: bytes=0-1' \
-H 'User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_12_2) AppleWebKit/602.3.12 (KHTML, like Gecko) Version/10.0.2 Safari/602.3.12' \
-H 'X-Playback-Session-Id: 820D13E9-4BEB-4C01-A0F6-59F95F0B9F8A'
The output from Safari's inspector: