please note that access denotes legal access, not safe or preferable routes. Road classification can be used to help with that

I agree that this is something the state would generally mark as no access by bikes horses and peds, but in this particular case, I'm not sure if there's the exact signage that is required (state law allows bikes on all public ways  except limited access/express state highways with signage specifically prohibiting bikes). I'm not going to argue with the way you've tagged this, just noting the oddity