You should be careful with this. Last time I saw an article about reproducing Shazam's algorithm, their lawyers came after them and eventually the article was removed.
There were questions as to the validity of the threats their lawyers used, but even a bulletproof case is a costly endeavor when going up against the scale of companies.
The title card of the video is "Please don't sue me", so I assume OP is at least somewhat familiar with the risks.
The Shazam patent is out there.
I'm curious who's better Shazam or SoundHound
Related I recreated Shazam’s algorithm with Go (494 points, 7 months ago, 117 comments) https://news.ycombinator.com/item?id=41127726
How Shazam Works (2003) [pdf] (117 points, 11 months ago, 29 comments) https://news.ycombinator.com/item?id=40029036 - there's a lot of links to past Shazam stories in comments