Do you need a Google account to opt out of the restriction? It says something about authenticating.

I don't have a Google account on my Androids. But I can't remove play services on them, sadly. As an intermediate protection I just don't sign in to Google play, that gives them at least a bit less identifying information to play with.

I hope this can be done without a Google account.

The reauthenticate means using device pin/biometrics if you have them enabled.

You will not need a Google account.