A self-sustaining reaction is exactly what happens with the fissionable material inside the nuclear weapon[0]. It seems like you’re trying to be pedantic on terminology here, but if you’re saying that a self-sustaining reaction is as un-scientific as a perpetual motion machine, you’re simply incorrect.

[0] https://en.wikipedia.org/wiki/Criticality_(status)

I'm pretty sure they didn't think the reaction would be perpetual; just long-lasting enough to wipe out life on Earth.

I assume the fear was an uninterrupted burn until the gas depletes, as in the Darvaza gas crater but atmosphere-wide.