[dtparr]

While you're correct that it's not a parody, parody is not the only form of fair use. From 17 USC § 107[1] "...purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright....".

1- http://www.law.cornell.edu/uscode/text/17/107

[adjwilli]

Was this video critiquing, commenting on, reporting news about, teaching or researching the song? No. It still doesn't qualify as fair use.

[dtparr]

A work need not target the original in order to be considered fair use, you have to apply test all the §107 factors. As Justice Souter put it in Campbell vs. Acuff-Rose Music[1]:

"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