I just noticed this same problem.

Alright, problem solved: I fixed it.
I went into the DayZ game files, specifically BattlEye stuff and started both of those services in the folder (I'm not sure which one was actually needed or if both were).
I also changed the permissions of the DayZ and DayZ_BE applications to run as administrator.
I'm guessing it was the BattlEye service that wasn't running. Anyway, the game opened so I can finally play again!

It loops between a windows permission screen and the small steam window that says launching a game. When I click no or exit out of the permission screen, this error shows up (I added a picture).

I've tried that several times before and it doesn't help. I did try it once more just to make sure :P

The only other option that I can think of is uninstalling the game, and also deleting and DayZ related documents (mainly the cfg, and DAYZPROFILE files). That way everything will start fresh.
I don't particularly want to try this as I not sure exactly what it will do.

EDIT:
I tried removing the DayZ folder in Documents, but it didn't help. (I just moved the folder somewhere else).