Vault Tek launched nukes because they were fearing of losing all their profits and dotations due to potential peace treaty with China.
They decide to do it during a corporate meeting with various companies (apparently that's the cameo appearance for House and Sinclair) and divide the Vaults between themselves to see who will rule post-war America.
NCR was completely destroyed after Shady Sands was nuked in 2277, completely retconning New Vegas (First Hoover Dam Battle should take place in that year). Only bands of marauders still carry it's name including the bandits that attacked the Vault.
The crater with Shady Sands library sign in trailer was the Shady Sands. It was not founded by Aradesh, but the leader of the NCR bandits.
The show ends with a shot of Vegas, but it's completely dead, including Strip casinos (so I guess this version of House did not prepare).