Next time you press a KB overhead with your right arm, put your left hand on your right chest. You should feel the chest muscles working.
I think there's two things going on here.I mean... on a press my glutes and calves are firing too. But I wouldn't call it good at developing my glutes and calves.
First: Without spending too much time into the taxonomy of muscles, I'd classify it almost as working vs training. I can feel my back almost cramping on a heavy set of max rep presses - and while I think the back is playing an important role, I wouldn't say it is being "trained" or is getting stronger (or bigger). The feeling my my shoulders and triceps is different, and I think they are being actively trained. Similarly, quads and glutes and even toes can contract very hard almost to the point of cramping during a maximal pressing activity - but I wouldn't say they are being trained so much as working.
Second: Technique. If you are arching your upper back and have some lay back, you will (likely) have more pec involvement. I have a decent amount of lay back in the initial 1/3 of a press, particularly with a barbell, and I would say that the pec is a little more involved than in the "working" examples above. It doesn't get "trained" to the same extent as when I do a bench press, but I think it is more trained than the back.
Again, I don't have a good way of defining and explaining "working" vs. "training." Feel free to tear that classification apart.