Modern "Infustrialized" war would be war on air,land, sea. So no I'd say WW-I was first. Every war in History saw many technological inovations so that alone cant describe it.
The Civil War wasnt that much different then the War of Independance. Soldiers still marched into battle in formation. The horse was still the major mover. Yes there was railroads, minnie balls, and rifled muskets. Eventually repeating arms and a type of machinegun.But "most" of the war was plain old front stuffers. But there was yet no mass production assembly lines. No high quality steel. No major naval engagement between modern Navies, no submarines, no airplanes, no tanks, no modern cartridges with spitzer bullets, no bolt action rifles, no hand held machineguns, no wireless communications, electricity, the list goes on and on.
Quite simply the machinery of modern war just wasnt there until WWl .
