"By contrast, when there is little or no risk of market substitution, whether because of the large extent of transformation of the earlier work, the new work's minimal distribution in the market, the small extent to which it borrows from an original, or other factors, taking parodic aim at an original is a less critical factor in the analysis, and looser forms of parody may be found to be fair use, as may satire with lesser justification for the borrowing than would otherwise be required."
Given that it seems fairly unlikely that there's a chance of consumers preferring this video to the original version of the song, the noncommercial use, and the length of the clip, I'd say it's got a pretty strong shot at being fair use.
1-http://www.law.cornell.edu/supct/html/92-1292.ZO.html#FN14