Does the video play correctly in any browser? Or is it like that in all browsers?
If you use a native video player program (Windows Media Player, VideoLan, etc) to view the file, does that work?
Something to try here to double check if it is Unity, or web browsers that would be at fault, is to create a small stand-alone video.html file with contents
and place that next to test.mp4, and then open the .html file in a browser. If that shows up correctly, then it is likely a Unity bug → please open a bug report with the test video file.
If that also shows up incorrectly, then it is likely a browser bug, or a system-installed codec bug. → report a bug to Chrome/Firefox/Safari.
As a workaround, I wonder if changing video codecs might help. Do you know which video codec the video is using?