Yep, the code executed via action menus is always executed locally (for the player or unit that activated the action).
On the other side, trigger's code is executed everywhere.
For example:
the code of your action would have only: action_activator = _this select 1;
the condition of a new trigger: !isNull action_activator
the code of your trigger: res = [action_activator]execVM"computer.sqf"
computer.sqf will be executed everywhere once action_activator has the unit that activated the action, and inside computer.sqf you will to check locallity of the passed unit to make sure the switchmove is executed only when local (_this select 0), as switchMove and playMove works only when passed unit is local.