Youtube is not the copyright holder, the RIAA's members are. They have licensed their content to Youtube.
Youtube stores cache files to a user's computer, obfuscated so they can't be easily copied or accessed, most likely as part of the terms of their license. That is legally sufficient to constitute a copyright protection scheme.
Material is covered by fair use and can be used legally in that way. Takedowns are for copyrighted material being distributed to provide immediate relief, the yt-dl projects code is not owned by riaa therefore riaa is abusing the legal mechanism.
Youtube stores cache files to a user's computer, obfuscated so they can't be easily copied or accessed, most likely as part of the terms of their license. That is legally sufficient to constitute a copyright protection scheme.