An elliptical adverb clause is a dependent or subordinate sentence that works as an adverb. What characterizes it is the fact that one or more words are implied. That means the words are missing from the sentence but we can "guess" what they are because of the previous independent sentence. That is precisely what we have in " I know how to play as many songs as he."
We can guess from "I know how to play as many songs as" that the continuation of the second clause is "[he] knows how to play". To avoid the repetition of verbs and expressions, we omit the words.
