No, vertical - it isn't. It all depends on what the manager is doing. 'CRM' as we know it sits in a very tight arena where interaction in a moving machine is concerned. It involves all sorts of processes like decision making, allocation of duties, awareness of personal issues like tiredness, illness, stress etc ALL related to the task of operating an aircraft.
'Managing' an operation on the ground involves many of these factors too, but in a totally different arena and requires quite different skills. Until s-s tells us a bit more about the 'job' this manager will be doing, how close to an aircraft he/she will routinely get, I cannot see any need for a 'Crew Resource' qualification here. Recognising that the work force are being 'stressed' is a management skill taught in a different school..