I think we should be careful with our language here. One definition of war is - "a state of armed conflict between different countries or different groups within a country."
Another is - "a conflict carried on by force of arms, as between nations or between parties within a nation; warfare, as by land, sea, or air. a state or period of armed hostility or active military operations: The two nations were at war with each other."
Clearly there is armed conflict but on a scale that is far from global. This conflict may well be a precurser to world war though. There is nothing unique about this, there were several conflicts pre 1939 involving Nazi Germany, Fascist Italy and Imperial Japan, but they were precursors not WWII.