Stylistically, both the Fallout series and Blackops were set in the fifties, so that's why you'd see the similar themes. Fallout just took 50's America and extended it for 100+ years. Good catch though.
Edit for clarification. The Fallout series took the themes and technology of the 1950s and made a separate timeline where America n progress stayed within the 1950's culture and technology. I.E. the cold war never ended, 1950's cars didn't stray from the styles of the period, and tranistors really weren't developed. Everything ran off of nuclear power.
Take a look at any documentary on the development of the nuclear bomb post WWII. Any good one will delve into the culture surrounding the arms race, giving you a perspective of what it was like.