Arguments and wars are different kinds of things--verbal discourse and armed conflict--and the actions performed are different kinds of actions. But ARGUMENT is partially structured, understood, performed, and talked about in terms of WAR. The concept is metaphorically structured, the activity is metaphorically structured, and, consequently, the language is metaphorically structured.

But really they're not, because they both share the metaphor of territoriality and domination.

Semantic territory and dominance are as important as physical territory and dominance. In fact you can't hope to win or own physical territory unless you have semantic and intellectual dominance over a significant population - who are then magically persuaded to wage a physical war for you.