When Stack Overflow refers to "moderators" it is referring to the people who have a diamond after their name who were elected as part of a moderator election.

These individuals are mostly doing things like stoping fights in comments, locking (not closing) posts that have debates on them, and investigating vote collusion so that people can't boost their rep from an alt (or coworker or spouse). On smaller sites (not everything is Stack Overflow) moderators are often involved in guiding new users as you can read all the posts from a day in a few minutes - for example Academia gets about 7 questions per day (Stack Overflow gets that many each minute). They also often run anti-spam tools.

Most actions that close questions (especially as duplicates), edit posts, ask questions in comments are from other community users (not moderators) who have rep from contributing to the site. Again, these are not moderators. Some members of the community have more of an interest to curate it to fit their ideal of what the site should look like (and that's a debate that goes back a long way).

It is the diamond moderatos who are going on strike. Some of the community are also further abstaining from doing things (answering questions, closing questions, doing reviews).

So the claim that it is the moderators that are going through and checking things and insisting that they are of the right form is misplaced. Moderators are rarely involved in dealing with the quality or content of a post unless that is brought to their attention by other users and there is a substantial problem with it (e.g. the person is posting with every variable name as a vulgarity and rolling back any attempts to edit it).