Via David Knight.
In 1945 Japan became wise to the Manhattan Project, they then convinced America (through counter intelligence) they had their own version of the atomic bomb and the means to deliver it to the west coast of the USA using a modified Sen Toku I-400-class submarine and launching atomic torpedo-like missiles (later tested by the US Navy under the 'Jupiter' guise), therefore creating a nuclear stalemate and not ending the war in august 1945. Home defence against a 'regular' invasion became thus even more important than it already was, and defending an empire consisting of lots of islands called for fast, water-borne aircraft for reconnaissance, interception and anti shipping missions.
As the N1K2 Shiden Kai was at that moment arguably the Japanese Navy's best aircraft it's understandable they choose that proven airframe to experiment further with, and so the N1K1/2 was born, and later proved itself even more important as being the first Japanese single seater to launch a heat seeking missile in anger: the Igo-2-A fired against HMS Irreplaceable of the British Pacific Fleet: she was hit and sufficiently crippled to be out of commission until just before the end of the war.
The N1K1/2 was designed in October 1945 (though it's the Igo missile that dates this specific plane to 1946).
but the design for the original N1K1 Kyofu is from 1944, and the N1K2 Shinden Kai (the wheeled version) first became operational in 1945.
The right, de-cockpitted side has a different, experimental engine from the engine on the left side. You can tell that from the different exhaust, the air-inlet just below the vertical stabilizer, and the lengthened fuselage.
The Missile:
The missile between the fuselages is a swept wing Igo-2-A Anti Shipping Missile, made by Mitsubishi. Introduced in the closing stages of the war (November 1946 to be precise) it uses infra red (thus the world´s first ´heat seeker´, with the first batch delivered to the Imperial Navy about 10 years before the AIM-9 goes into production), has a solid-fuel rocket, and is small enough to be launched from fighterplanes instead of bombers.