Probably not related but these cartridges resembled 8-track cartridges which were also often referred to as (8-track) cassettes. It is easier to capitalize on slang than to make up a new word in marketing. Cartridge may sound too technical or even gun-like.
I suspect that the term "cartridge" being used for 8-track shells may be the source of "cartridge" describing the packages that ROM-based games came in, especially given the resemblance between 8-track cases and those of Atari 2600 games.
I think usage of these terms became a bit calcified much more recently than we think. My first computer was a TI-99/4A, and while the term "cassette" was used regularly in its literature to refer to using audio cassettes for data storage, the ROM cartridges that commercial software came on were never called "cartridges" officially, always "solid-state software" or "command modules", with this usage extending well into the '80s.