He is very good at accompanying people singing with his guitar

“He is very good at accompanying people singing” is a perfectly good sentence. The sentence “He is very good at accompanying people singing with his guitar.” can be criticised because it appears to say that people are “singing with his guitar”. That would make no sense. It’s something that might easily be spoken, but it would be much better as two clauses: “He plays the guitar and is very good at accompanying people singing.”

In the original text that explanation is not needed – we already know that he is an accomplished guitarist, so “He is very good at accompanying people singing” was all that was needed.