Short of trying to contact whoever produced the original video clip (as they might be able to indicate where it was licensed from), the answer is sadly no.
Shazam (or any other similar service) has to have ultimately heard of the track previously to be able to find a match.
AcoustID will not help you here either as its likely an edited down version.
Along with that MusicBrainz has a fair amount of “library music” in the database, but not a fully exhaustive list.