Youtube does not use the DMCA nor does it comply with the DMCA.

The DMCA requires the service provider reinstate the content 14 days after the dmca is contested unless the claimant follows through on the claim by filing a lawsuit in court. Youtube does not do this.

The DMCA also explicitly states that it's protection against liability doesn't apply to service providers that do not properly implement the counter-claim reinstatement process, and as such, youtube is not covered by the dmca's shield.