The purpose of a patent is to encourage global innovation by granting exclusive rights for commercialising technology for a limited time in response to sharing how it works.
Roughly, if you invent PageRank and keep it internal to your search company, you can exploit that idea but if someone else comes up with it they can exploit it too. If you invent PageRank and patent it, the whole world knows how it works but can’t use it for 20 years without paying you.
Generally in case of a violation you’d want to sue for damages, whether that be licensing costs not paid, or missed revenue on your own side.
This probably then ends up in a bit of a grey area. Shazam would be within their rights to exert the patent, but the damages are likely so minimal to be outweighed by the cost of litigating the case, which means that the C&D is a little too chilling for my liking. Basically, any penalty would be lawyers fees - author hasn’t tried to commercialise it, it doesn’t reduce Shazam’s revenue at all. Are there any damages at all?
And then, few would argue (I think) that simply implementing a patent for educational purposes constitutes infringement. My uni course contained an implementation of PageRank. Is publishing the course notes then infringement? Arguable it’s anti-goal to discourage actually spending time learning about the innovation beyond just reading the patent doc - otherwise the motivations of the system break down. So, just how different is this? Presumably on a conceptual basis you want your universities to be able to teach about things invented in the last 20 years without licensing patents?