Ok, now I can at least understand why Japan did not immediately declare war on the planet.
1 Lack of information about the planet
(borders, nations, inhabitants, resources) You could declare war, but the moment your fuel and ammunition runs out, you're left defenceless in a world with Magic. So good on them for making that call.
2 Common tongue
(extremely lucky for the planet) I can imagine if the planet did not speak Japanese, this could have caused hostilities thus leaving Japan no other alternatives but to be more defensive in their decision making.
Now for the reason I think it was wise not to assist a wartime plea immediately is part of the above.
Japan does not know the resources which can be gained in helping or supporting a war. Does the enemy have oil in their lands? (much like how US likes to get involved), it's a waste of resources and troops if there is nothing to be gained in their involvement.
Also for the sake of creating strong ties with the planet, the enemy might also have some resources that the current nation does not, so playing both sides could be beneficial in getting more resources/information on the planet.
But in all honesty, I'm still in the belief that Japan would declare war on the world still. Once all the necessary information has been gathered on the planet, I really do not see any reason why a nation with a powerful military would not choose to expand, especially knowing the extremely large gap in strength, and that a modern nation need resources to survive. It's only a matter of time in my opinion.