1. Copyright owner provides written notification of the alleged infringement.
The notification has to provide reasonably sufficient information to allow Google to locate the alleged infringing material; provide contact information for the claimant; include a statement that the claimant has a good faith believe that the use is not authorized by the copyright owner, its agent, or the law; and a statement that the information the claim is accurate, and that the claimant is authorized to act for the owner.
2. Google then has to remove or disable the material, and take reasonable steps to notify the uploader of the issue.
If the uploader does not make a counter notification, it looks like that's the end of Google's obligations.
If the uploader files a counter notification, Google has to notify the claimant. If the claimant does not file a lawsuit against the uploader within 14 days, Google has to restore the material.
Note that nothing in here seems to require Google to actually look at the material and decide if they think it is infringing. Nor does it require them to proactively seek to find infringing material and notify content providers or block such material. They just have to check that the claimant (and the uploader if they get a counter notice) have included the things in their notice that the law requires. They should be able to automate that for most claims.
The ContentID system seems to be going far beyond what DMCA requires them to do to keep their safe harbor. I wonder why they are doing that? Maybe because they want to also be content sellers, and so want to keep the content providers happy with them?