Atompunk is the dark version of 50's era astro-futurism, like in the Fallout games.

The "punk" moniker suffixed onto genres generally implies tones and/or themes one would associate with the punk movement, e.g. anger at a corrupt system, anti-authoritarianism, anarchist ideals, etc.

I'll agree the usage is oversaturated, though, and is sometimes only used to convey "dystopian"