I don't think there would be a royal union -- Japan had been absorbing white racial attitudes for decades, and the religion problem (Christian Ethiopians, divine Japanese Emperor) would be a major sticking point.
Now, what I could see is Japan helping out or supporting Ethiopia as part of a larger anti-European alliance. Of course, this alliance would itself be imperial, but Ethiopia could be in East Africa what Japan tried to be in Asia.
All of this is contingent on Ethiopian stability; unlike Japan, Ethiopia at the time was riven with religious and political conflict, generated by nearly-autonomous princes. If these conflicts are stopped or crushed, Ethiopia could have a decade or three of military advancement before the conflict between the Japanese bloc (Japan, Ethiopia, maybe Thailand, even a Euro country) and a European imperial bloc.
I'd guess we'd see the Entente defending a weakened China (France and Britain also have colonies to defend) vs. Japan, Ethiopia, Thailand, and independence movements in Indonesia and India. Germany would be a key European ally at this point, and I could imagine German industrial and military aid helping buff up Ethiopia.
The Soviets at this point would be neutral. Italy would be a wild-card, probably French leaning. I don't think there would be a European war; Germany would have no southern ally and would be surrounded on all flanks. Not to mention Hitler could be butterflied away.
Ultimately, I think this would end up less as a World War and more like the Cold War; Japan gaining influence in the post-colonial world as France and Britain bleed to death defending Empire.
Soviets would probably be limited without a world war to give them traction; I see them probably trying to carve out a puppet or sphere in China and supporting Communist revolutions in Korea and elsewhere. Heck, if America stays aloof we could see a Russo-Japanese Cold War over the post-colonial sphere, although a less imperial America means that our brand of democracy loses less of its luster.
The long-game would basically revolve around which models and spheres the post-colonial world adopted. Europe is less burnt out but probably less relevant politically; America is probably neutral but facing Latin American dissent, with some friends scattered, big on capitalism; Japan has their sphere but faces independence movements itself, and the Soviets fund radicals and slowly watch their economy fall apart (although Japan's economy wouldn't be much better).