That link is for actual DMCA notices. With the Content ID take-downs, Google never actually receives a DMCA request. The music company (etc.) politely asks YouTube to take down the video, and YouTube complies out of the goodness of its heart. (Well, and a bunch of contracts that give some sort of quid pro quo for the arrangement between YouTube and these companies.)
It looks like these are all Content ID takedowns (well, actually not takedowns; whoever is making the requests is taking the ad revenue from the videos, but leaving them up). In these cases, YouTube has their own dispute system, but it doesn't touch the DMCA.
I think this is the relevant page: https://support.google.com/youtube/answer/6013276?hl=en&ref_...