"This was not a DMCA 512 notice."
It is remarkable how few people commenting on the web are noticing that.
A notice under section 512 needs to identify both the material infringed and the infringing material.
The letter identifies some works that may be infringed, e.g., VEVO videos listed in youtube-dl's documentation.
However it does not identify the location of any infringing material, e.g., an unauthorised copy of a VEVO video.
It cannot be a valid DMCA 512 notice.
The letter instead refers to section 1201 which includes a prohibition against enabling circumvention of copyright protections.
The argument is that youtube-dl violates that prohibition.
Online debate about the applicability of the DMCA in this case should focus on section 1201 not 512.
For example, is youtube-dl "primarily designed for the purpose of circumventing a technological measure that effectively controls access to a work protected [by copyright]" Do most YouTube video URLs use enciphered signatures. Not IME. Does the rolling cipher "control access" to YouTube videos, or does it just control downloading. Etc.
1201. Circumvention of copyright protection systems
(a) Violations Regarding Circumvention of Technological Measures.
(2) No person shall manufacture, import, offer to the public, provide, or otherwise traffic in any technology, product, service, device, component, or part thereof, that-
(A) is primarily designed or produced for the purpose of circumventing a technological measure that effectively controls access to a work protected under this title;
(B) has only limited commercially significant purpose or use other than to circumvent a technological measure that effectively controls access to a work protected under this title; or
(C) is marketed by that person or another acting in concert with that person with that person's knowledge for use in circumventing a technological measure that effectively controls access to a work protected under this title.