Dictionary definition of war: "a state of armed conflict between different nations or states or different groups within a nation or state."

Its clearly a conflict. Its clearly armed; both sides are shooting weapons at each other. Israel is a state. Hamas is a bit less clear cut but its the defacto government of gaza, which isn't technically a state (edit: debatable, maybe it is technically, idk), but is at least a self-governing territory.

Sounds pretty war-ish to me.