just did some close grip bench today for my arm day.. for the close grip, i'd say i would NOT count it as a chest exercise if you are doing it correctly, elbows tucked in throughout the motion. That is my personal opinion. Yes, it obviously requires your chest to do a little work, but it should not serve as a chest exercise. I've never gotten a sore chest from it.
Close grip chinups will work your back, if you focus on form and "pause" at the top. if you pinch your shoulder blades at the top of the movement i could see it giving your back a decent workout. But as with the close grip bench, i would not suggest replacing your standard back exercise, such as pull-up or wide grip pullup with a close grip if youre trying to hit your back. both the wide and standard grip blast your biceps as well as your back, so why not do one of those?
in summary, ADDING them to a chest or back day would be fine, but if that comes at the cost of removing chest and back focused work, i would not recommend it. OF COURSE, that is in my humble opinion in what i have personally seen in my work at the gym. someone may post below me and refute me claims, dont be mad