US/Israel and Iran each have millions of military and military-industrial personnel, and yet the actual combat is being performed by a few thousand at most. There might a thousand people in uniform for each one directly engaging the enemy (flying a sortie, launching a missile, firing a torpedo) on any given day.
So these nations are at war, but the ground troops aren't invading in foot? Instead, they're in barracks or never raised to begin with? What relevance could this have to the quote from Gattling?
Probably the same relevance as the type of war you're referring to (asymmetrical strike exchange). The war of conquest between countries of comparable population and military power Gatling referred to still needs a lot more people on the ground doing the actual takeover part.
So how might a global and region powers engage in a war without engaging in territorial invasion? What kind of advancement might allow such a conflict to take place with only a tiny number of combatants?