One of the first movies to leverage the idea of radiation- it came out the same year the Godzilla debuted in Japan, and two years before Godzilla came to the US theaters.
The effects are rather impressive when you think about them. Full sized bug puppets, which is more effort than many films which just super imposed footage of real spiders or bugs against actors. The giant puppet ants were able to grab and attack actors, which brings to mind the bug animatronics of Starship Troopers.
The plot and execution is pretty good, and the early mystery is actually quite creepy as the investigators uncover ransacked isolated buildings and vehicles with no sensical explanation for the destruction.
Have to give a partial nod to The Beast from 20,000 Fathoms (1953) - radiation doesn't cause the monster in that one, but a nuclear test wakes it up. And the fact that it made a bunch of money (following on from a 1952 reissue of King Kong, originally released in 1933, that did pretty well) is probably partially responsible for Them! being made.
Understandable that the nuclear program (let alone the bombings in 1945) would kick off a "science is dangerous" trope, but I feel like that went on too long and probably fostered mistrust in science to an unhealthy level for decades (yes, I know Frankenstein probably started it).
But I agree with you, Them! is actually a pretty good movie, especially for the time and genre.