Bas Aarts link explaining function in order to explain why 'white as a sheet' is an adverbial

I have been asking about the passage below - and it is a genuine query:

"At ten o'clock she stood up to retire. Everyone rose with her, and to Roger's sudden consternation, she held out her hand for him to kiss.

White as a sheet he bowed over it and touched it with his lips."

(It comes from a novel by Dennis Wheatley.)

The reason why I've been asking, is for an explanation as to why the phrase 'white as a sheet' is  an 'adverbial', when it appears to be describing or 'qualifying' the pronoun and subject of a sentence, 'he'. That sounds to me  'adjectival' ie doing the job of an adjective. Perhaps I'm wrong. 

In other words, I'm asking a question about this kind of grammar on its own terms. This particular matter arose out of the Grammar Day at the British Library on Monday. When I raised this here, Professor Bas Aarts kindly sent me a link to his blog. 

https://grammarianism.wordpress.com/2015/09/11/form-and-function/

I'm being honest when I say that I can't see how this link explains why 'white as a sheet' is in fact 'adverbial' in function. 

I note that in all the examples given of adverbial function, it shows words, phrases and clauses behaving adverbially. I haven't seen a construction like 'white as a sheet, he bowed...' included under the function 'adverbial'. 

Here are some more links on the different kinds of grammar that can be used to discuss structures of sentences:

https://en.wikipedia.org/wiki/Grammatical_relation

https://en.wikipedia.org/wiki/Dependency_grammar

https://en.wikipedia.org/wiki/Phrase_structure_grammar

 Here's a link on some competing theories:

https://en.wikipedia.org/wiki/Predicate_(grammar)