Google accepted a DMCA request for the homepage of the Android streaming app NewPipe. Its homepage newpipe.net has been removed from Google search results if one searches for "newpipe". NewPipe is an alternative privacy focused YouTube frontend, but also supports other services like PeerTube, SoundCloud and Bandcamp.
The way the DMCA works, to my understanding, Google has to accept the notice, unless NewPipe submits a counter notice, which can be done here: https://support.google.com/legal/troubleshooter/1114905 Proceed as if reporting infringement, and the option will appear to specify this is a counter report. If the reporter chooses to continue, the next step is with the courts.
They don’t have to accept it-they can choose to ignore or reject it. However, if they choose to ignore/reject it, and the notifier then sues them, they may lose one of their legal defences.
Obviously they decide that most of the time complying is the legally less risky path, so most of the time they comply. However, if they get a DMCA request for a famous website like nytimes.com, they probably won’t action it.