If tug of war was about the force vectors being added together, pulling sideways should be equally effective to pulling in any other direction, I think. (Imagine the rope is under so much tension from the preexisting pullers that you can model it as a steel bar. Further imagine that you are on a frictionless plane and everyone is exerting force via rocket thrusters. Your own little thruster will slowly accelerate the whole system equally fast in whichever direction you pick.)
If tug of war was about the force vectors being added together, pulling sideways should be equally effective to pulling in any other direction, I think. (Imagine the rope is under so much tension from the preexisting pullers that you can model it as a steel bar. Further imagine that you are on a frictionless plane and everyone is exerting force via rocket thrusters. Your own little thruster will slowly accelerate the whole system equally fast in whichever direction you pick.)