Modern-Day Countries of the Mayan Empire on a Map

That doesn't make them an empire. Also do you have a source that the Maya cities almost never fought against each other? This wiki page doesn't seem to support that claim.

Maybe during the absolute peak of the power of the League of Mayapan, which was a loose alliance of Mayan city-states that controlled most of the Yucatan, you could argue that they were in any way fighting together or unified, but that alliance did not control anywhere near as much territory as shown here, and it was only dominant across the entire peninsula for around a half century or so, before beginning to disintegrate, though it remained a regional power in the northern third of the peninsula for a few centuries.

We have plenty of accounts of Mayan city-states fighting one another. The Classical Period of Mayan History is more or less defined by the continual wars and proxy wars between the rival city states of Tikal and Calakmul, with induvidual wars going on for decades.