We see in these examples the following pattern:
[subject] [verb] [argument1] as well as [argument2]
In the example from Practical English Usage, the [verb] is the auxiliary have to. It could have been have to feed, if the part after the as well were a valid argument to feed, but it isn't. So it could have been:
I have to feed the animals as well as the children
In that case, I have to feed would distribute over the animals and the children, meaning:
I have to feed the animals and I have to feed the children.
The PEU example means:
I have to feed the animals and I have to look after the children
Here, the verb have to is distributed over the two arguments, each of which is a verb phrase.
The sentence you are concerned about means:
He is an excellent teacher and he is a fine musician.
Obviously, there is a shared is in this sentence, so we can take that out and distribute it over the two arguments, an excellent teacher and a fine musician:
He is an excellent teacher as well as a fine musician.
The verb appears after as well as in the PEU example because the argument to have to is a verb phrase, while in the teacher example the argument to is is a noun phrase.