"...man exists because a cosmic accident blew away most of the gas that a body its size ought to have kept, as Venus has done." (p. 11)
Sf readers read then-current scientific ideas in sf stories. This story was published in The Magazine of Fantasy and Science Fiction in 1971.
Ideas that I have read elsewhere are that:
Lunar gravity thinned the Terrestrial atmosphere (this is crucial to Larry Niven's "Wrong Way Street");
tides, also of course caused by Lunar gravity, facilitated the evolution of amphibians and the transition of life from sea to land;
the Moon maintains the Earth's magnetic field (see here).
The Earth-Moon system is a double planet and the Moon almost certainly has other effects.