It works for both the steam and non-steam versions. Though you cannot use the play button.
Process for non-steam version.
The updater settings should be changed so that ARMA II Folder:
C:\Program files\Bohemia Interactive\ArmA 2\
exactly as above. Leave the download URL alone. dont change that.
Create a brand new shortcut on your desktop. put this as your target path:
"C:\Program Files\Bohemia Interactive\ArmA 2\arma2OA.exe" -noSplash -mod=@dayz
exactly as above. Name it something like DAYZ Mod