The exact grammar is tricky. In part, this is because ‘-ing’ words are tricky. It is not always certain whether they are functioning as adjectives (and so are called participles) or as nouns (and so should be called gerunds).
If Conan Doyle intended a participle, he could have made it clear by using a comma after ‘intelligence’.
The matter was simplified by Brunton’s intelligence, being * quite first rate.
If he intended a so-called ‘gerund’, he could have made that clear by adding an apostrophe to the word ‘intelligence’.
.... by B’s intelligence**’s** being quite first rate.
In terms of meaning, I cannot see any difference. Holmes is making an inference from B’s first rate intelligence.
But each alternative construal has an objection. I should be surprised if Doyle, at the time he wrote, would have omitted a comma after ‘intelligence’, if he had intended “being quite first rate” to be a participle phrase, qualifying ‘intelligence’, Every schoolmaster in his day was very fussy about that sort of thing.
The same objection applies to the alternative. In Doyle’s time, The omission of the possessive ‘apostrophe ess’ after ‘intelligence’ would bring down the scorn of many a reader on his head.
Of course, there is a reason to avoid this latter option. It lead’s to a horrible double possessive.
... Brunton’s intelligence’s being quite first rate. (yuck! He would never do that.
Where does that leave us? Well, we could just ignore it. It makes no difference to our understanding. My guess, for what it is worth, is that there is a comma missing. I cannot imagine Doyle, living when he did, either omitting to write “...intelligence**’s** being ...” or tolerating the cacophony of “Brunton’s intelligence’s being first rate.”.
So my searchlight would switch to the version of the text you are using. Doyle is out of copyright; anyone can publish; many cheap internet editions circulate; fewer editors have the old fashioned grammar that might lead them to spot an error and check. Ironically, the combination of universal literacy, computing and the internet has taken us back to how it was in late antiquity and the early middle ages, when hosts of monastic scribes were copying Latin texts, riddled with little errors of this sort.