I changed the .mp4 extension of my video to .mpg and it still opens and plays fine (in VLC and in Windows Media Player). Why is this so?
The .mpg and .mpeg extensions are typically associated with MPEG-1 and MPEG-2 files. The structure of these files is different than the .mp4 format used for H.264 video, part of the MPEG-4 family of formats.

I suspect VLC and WMP can play the file because they must not be using the file extension to determine file type, they probably parse the file with all the supported parsers until one works. To prove this point, I took a .wmv movie and renamed it to .mp4. When I played it in my Windows 7 PC with WMP I got a warning window saying that the extension did not match the format, but I told it to proceed anyway and the file played just fine.

If this online service requires MPEG-1 or 2 then you should transcode your video to one of those formats before uploading. Unless the online service transcodes all uploaded videos to some standard format. In that case it does not really matter what the format of the uploaded video is, as long as the service can read it and transcode to its own favorite format.

Good luck.