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A. David being the chairman has meant more work for all of us.

I just came across sentence A on this site : Prepositional Phrases as Subjects @ The Internet Grammar of English (ucl.ac.uk)

But according to whether commas are inserted or not, does the meaning of sentence A change?

B. David, being the chairman, has meant more work for all of us.

I think that without commas, "being the chairman" defines what kind of person David has been, but with commas, "being the chairman" seems to work just as additional information without the sense of defining.

Am I right?

And as a side question, are both sentences A and B correct?

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B doesn't make sense to me. Maybe it's too metaphoric for me to think "David" means "more work of all of us". So I think the question about A and B would make more sense if you had "has made" instead of "has meant". But that may be beside the point.

Anyway, without commas "David being the chairman" is the subject of the sentence. It's a gerund clause. More formally, "David's being the chairman". It means "The fact that David is the chairman".

And with commas "David" is the subject. It's an ordinary noun phrase (NP). "being the chairman" is then a participle clause anchored on "David". The relationship, as I see it, is causal. Thus "David, being the chairman," means "Because he is the chairman, David".

Others may prefer other interpretations.

CJ