That's what the TV show is saying.
In the games, Vaultech does not exist in any way following the war. And certainly would not have private nuke silos.
The TV show is operating outside of the established game story. Which is fine, it's just how fictional stories work sometimes.
In the GAMES, the story put forth in the TV show is simply impossible. So there is no precedent in the games for explaining the show. Or providing context to what might happen next. The NCR is multi state spanning society. Not one big city with a corn field outside of it. A nation large enough to have the societal and human capital to go to war all the way into Nevada. No vault, let alone 3-4 in the greater LA area would still be closed at that point in history. The NCR would have popped them open, absorbed the population into the NCR, and taken the tech and valuables.
That's frankly why the games went to the east coast; the west coast was a wrap. On the west coast, humanity had prevailed against the apocalypse, in the form of the NCR. The only unexplored country was the east coast. Even the Brotherhood that's represented in the show is the East coast brotherhood returned to California, the west coast brotherhood died out and was destroyed or absorbed by the NCR. And the East Coast Brotherhood would not have uprooted and made that journey on a whim either.
Now, the game makers own the IP, so they can decided to "make the show fit" by retconning multiple elements of multiple games moving forward. But that's an after the fact decision. Not the TV show writers choosing to operate inside of the established world. It would be the game developers choosing to change and alter the game world to fit the new TV show plot.
What the TV show is, is the amalgamation of the environments from games 1 and 2 on the west coast, with the set design and visual assets from fallout 3 and 4 that took place on the east coast, including the East coast brotherhood look and style.
The story you get from those mashups, by default, can't exist in the established game world. They're even radically changing how gouls work in order to get certain story lines out of Goggins' character. So looking to the games for answer or guides to what will come next in the show, is at best, like looking at an old run of Superman comics to know what's going to happen in the rebooted story line. Is there going to be some overlap? Sure, maybe. Lex Luther is Probably still gonna be a bad guy, but beyond that, it's not very helpful to go diving too deep.