I doubt very much that there will be a war over this issue. I suggest you have to see this issue in the context of Obama's policy of 'pivoting to Asia' and the USA as an existing hegemon, marshalling the nations it controls to cause trouble.
However, in a future post I will explain why this territorial dispute is an issue. But note also that it divides the allies of the USA as much as it causes problems for China. South Korea and Taiwan are both opposed to Japan on this territorial issue. It also involves Russia. The island named Sakhalin to the north of Japan is also a disputed territory.
The background to all these disputes is very complex, but centre around the re-balancing of world affairs during the 19th C when European imperialism reached its peak (so the crises we have now are the embers of that period as the last "European" power of significance (the USA) (IMHO, Russia is more Asian than European- though I admit its arguable) attempts to maintain "European" control of the world.
For the moment, I'd like to focus on the island of Sakhalin. It came under Russian control as part of Russia's conquest of Siberia, mainly in the 18th C. (you will recall this extended as far as Alaska-later sold to the USA, without a democratic vote-grin).
In the late 19th C the Japanese elites made a decision to permit western influence. They quickly adapted (modernised) and by the turn of the 20th C found itself in conflict with Russia over control of Manchuria (Picking over the carcass of Imperial China). In 1805 war broke out between Russia and Japan. In a surprise attack (no declaration of war) Japan neutralised the Russian Eastern fleet and then a second. In the treaty of Portsmouth, Russia ceded half of Sakhalin to Japan.
In 1945, in the lightning, and very powerful attack on Japanese held Manchuria, Russia (now the USSR) decisively defeated the Japanese Army. From August 9, soviet forces sped over a landmass the size of Europe, including the Korean Peninsula. Only a last minute request from the USA, prevented Russia conquering all of Korea. Why the Russians agreed to the American request is something of a mystery. In the resulting peace negotiations Russia took back the half of Sakhalin previously ceded to Japan. From cold war days, (with some support from the USA) Japan has been asking for Russia to give it back.