The bombs fell in 2077, but it's an alternate Earth, not ours. On that Earth, after their version of World War 2, nuclear energy was rapidly developed and was widely used as a power source. Everything looks like it's from the 1950s, and the music is mostly late 40s early 50s. The game designers wanted to keep that retro look from the beginning of the atomic age, so even though 120 years or so passed before the bombs fell, everything still has that 1950's look. The cars look like 1950's cars, but they're powered by compact nuclear reactors. The big armored suits are powered by a fusion core which is basically a nuclear battery.