Bit of a misleading title by Reuters. They accessed the business networks of the NNSA, the agency responsible for maintaining the nuclear stockpile, but did not access the networks managing the actual nuclear weapons, as the title half-implies. There was no threat of random nuclear weapon exploits, those networks have not been compromised as far as we know.
Yea, also, who would build a nuclear bomb that could be detonated via the internet? I would be outright shocked if there wasn’t a mechanical part of the process... eg, in the early days, they literally had the warhead and bomb parts physically separated