The root loop is definitely per process. It’s simply the primary thread started up by Windows for a process in which the GetMessage(), TranslateMessage(), DispatchMessage() Windows API calls are made over and over again, with minor LabVIEW specific adaptions. This thread is associated with a hidden window whose window procedure then translates everything into a Platform independant message infrastructure that very much resembles the Mac classic message loop. This is basically the famous root loop with the message procedure in the hidden window being a sort of platform wrapper around it.
Under Windows there comes in a potential extra complication as the OLE marshalling hooks into the process GetMessage() API, completely outside the control of LabVIEW. So if you interface with OLE/COM/ActiveX and to some extend even .Net compenents things can get interesting,