Well personally I'm an ancap so I consider all laws/executive orders to be implicitly (and often explicitly) backed by the police power of the state. You can say that the government requiring employees to be vaccinated isn't violent police power because they're not holding them down and injecting them, but what exactly will the state do if the employer doesn't comply? They'll send in the guys with guns to enforce.

Really it's such a small thing to be splitting hairs over though. If you prefer, just read what I wrote and mentally s/violent police power/coercion