How about "The people like cars"? Is it a correct translation (or is it correct English at all)?
The people is not very correct because you are talking of people in general so you don't say "the people "such as you don't say "the cars"but "cars"
The translations of машини were only "Car", "Cars".
But should I report it since "machines" was also correct?
Yes, "machines" should be accepted too, it's worth reporting it.