Nintendo dead would probably fatally wound the Japanese gaming industry, they would survive but mainly retreat to mobile gaming and the occasional PC game either based off popular franchises or visual novel/anime/manga tropes. People think that Nintendo failing would force them to go third party, but it would mainly force them to retreat back to Japan and if truely dead, sell off their properties and lay off employees. The IPs and the employees may go else where but no telling if in their new landing spots they will be able to recreate Nintendo style gaming in a situation where they could succeed. Other Japanese publishers seeing the giant fall will only get more conservative and aim towards the elusive Western gamers or the mobile gamers.
The Western industry would continue onwards towards the current trend of being a shadow of the PC gaming industry and within 5-10 years, all gaming would be done via Steam or a Steam like service, with the few bright spots being indie development that would try to recapture the glory years of gaming with their own ideas based on games of the console industry's past. The rise of development costs will ultimately cripple all but a handful of publishers who will stick to certain genres with few to no experimental titles.
Edit: This is all speculation but based off how the industry has progressed, it is highly likely to come to pass.
