i can not download the mp4 from it seems like the file is damaged or so... i don't really know. but you are probably right that it just isn't possible to display it properly due to it's color limitation. one way to work around this would be to make the original file less color intense and have solid colors for the logo and background it would be less fancy but could eventually look better... maybe try it out...
you could try: https://cloudconvert.com/mp4-to-gif but i don't think it will change anything given the above..