Open war would be disastrous for all concerned. The North Koreans surely realise this. They're just pushing the South to gain more concessions. They think they have a stronger hand than the South. Also, there's almost certainly an internal political game being played here; the succession problem is looming, and the Dear Leader wants to appear strong and retain military support for his anointed successor.
A war would undoubtedly end in North Korea's collapse. But the consequences for the South would be just as devastating.
There would have to be reunification; a full-scale war would end with the overthrow of the current regime. North Korea isn't capable of standing on its own feet; as it is it's propped up with international and South Korean aid, including food for its populace.
The Chinese would doubtless set a number of conditions, but overall they probably wouldn't have too much of a problem with reunification, in the sense of intervening militarily, provided no US troops were stationed anywhere near their border.
The reason for this is simple: even if the South wins, it loses. Seoul, the economic and political capital of the Republic of Korea, is extremely close to the 38th Parallel. A war would be catastrophic. Even assuming Seoul is largely untouched, which seems unlikely given the vast number of batteries and missiles aimed at it, the North is so backward and undeveloped that it would be a serious drain on the South Korean economy. East Germany was bad enough, but it was far more developed than the DPRK.
Further, the whole rationale for US forces being present in South Korea (to the total of about 28,000 men) is to protect the South from North Korean aggression. Remove North Korea from the equation, and it's an open question how long those troops will remain there.
"Into the face of the young man who sat on the terrace of the Hotel Magnifique at Cannes there had crept a look of furtive shame, the shifty, hangdog look which announces that an Englishman is about to talk French." - P.G. Wodehouse, The Luck of the Bodkins