I'm not sure I understand why "he" is translated as "jeho" here, instead of as "on". Is it that "zajímat" means more like "to interest" or "to be interesting to", and not so much "to be interested in"? Because it would make more sense to me if "the machine does not interest him?" were an acceptable translation, too.
I think this is an example of a time when you need to let go of the idea that every phrase has an exact translation into another language. I mean, mit rad would be literally translated as "to have gladness" or maybe "to have joy" (I'm drawing on my Russian, I don't know exactly what rad on its own translates to, but the equivalent words in Russian would be something like to have gladness), but "Kateřina doesn't have joy in him" would be a terrible translation of Kateřina ho nemá ráda, because that makes almost no sense in English; we translate it to "Kateřina doesn't like him."
Not everything is going to "make sense" in English, and sometimes the natural subject/object construction of a sentence in Czech will be the opposite to what it is in English. In my experience, attempting to make sense of it in terms of "trying to make it fit English paradigms" is usually unhelpful. If it helps you remember that to be interested in is the opposite way around to what you'd expect in English, great (and if this phrase works both ways, fantastic), but that doesn't mean that a given translation should necessarily be different or more literal just because it makes more sense to an English speaker.
I think it's the same reason there's no preposition in the (very direct) English translation, "Does the machine does not interest him?" In this Czech sentence, "machine/stroj" is the subject and "him/jeho" is the object. The translation given on this page, "Is he not interested in the machine?", means the same thing but it swaps the subject and object which might make you think you need a preposition. Just like in English, you need a preposition ("in") when you say "I am interested in that", but no preposition when you say "That interests me."