GitHub has voluntarily instituted its own takedown procedures for violations of that section, and therefore do not actually need to strictly follow the procedure outlined in the law. Instead they can chose their own procedures for handling these claims based upon percieved likelyhood of being sued and being found liable.
Mircosoft is likely fairly confident that the RIAA will not sue them over this, since the other RIAA members (the Labels) all know that if Microsoft chose to enforce their huge pool of rarely enforced software patents against the labels and distribution mechanisms (like Spotify) the harm to their bottom lines would be many thousands of times larger than any harm to their bottom line from youtube-dl could ever be. Heck even just a more thorough than typical Mircosoft Software audit would likely be more costly to the labels than youtube-dl.