You're doing more than you need to for your arms but you're not overtraining them.
He's definitely doing more than he should be doing for arms but I wouldn't say that he's
not overtraining.
If you have some lifting experience you should be able to tell if you're overtraining. If you keep feeling fatigued when you hit the weights or if you can't get a quality pump, these are a couple signs that you're overtraining. You could even be doing less than what would illicit overtraining but still doing more than you require.
Personally, I do about 2-4 total sets for biceps per week and about the same for triceps. I do this because I already know I'm getting a lot of biceps work when I work my back and the same thing for triceps when I work my chest and shoulders (any time you straighten your arm against resistance, you're hitting your triceps). I like to add a few sets of arms-specific work to my routines so that my arm muscles are getting some work through their full range of motion. For example, when you do rows you're involving your biceps to a great degree but you're not working them through their full range of motion.
I recommend doing the minimum amount of arms-specific training because in my own experiences my arms get the most results when I do the least amount of direct work. If I could, I'd work arms all day long but it doesn't really work that way. Think of it like this... If a LOT of arm work got great results you'd probably see more people in the gym with great arms, right?
Try just adding a few sets for arms per week (depending on how your split is) and see how it works for you.
More often than not, less is more. Just make sure that "less" is intense and deliberate. Be strategic.
Good luck bro! Shoot me a PM if you need anything.
Peace