Does "entertain about" mean "distract about" or "entertain because"?

Question

In "The Quick One" by G. K. Chesterton, Father Brown was talking to his friend about a murder that happened in the hotel lounge after a very serious altercation between two men because of another man's speech about the teetotalism saying:

‘Well,’ said Father Brown, with broad-minded calm, ‘you started by talking about fanatics; and how a fanatic could do anything. Well, I suppose we had the honour of entertaining in this bar-parlour yesterday, about the biggest and loudest and most fat-headed fanatic in the modern world. If being a pig-headed idiot with one idea is the way to murder, I put in a claim for my reverend brother Pryce-Jones, the Prohibitionist, in preference to all the fakirs in Asia, and it’s perfectly true, as I told you, that his horrible glass of milk was standing side by side on the counter with the mysterious glass of whisky.’

Does "entertain about" mean "distract about" or "entertain because"?

And does "put in a claim for" mean "I'd choose .... instead of"?

And I'm a bit confused about the whole meaning that he wanted to convey, as this reverend brother wasn't the killer, and Father Brown knew that already!

Answer 1

"Entertain" and "about" are not linked. They (honestly, in this case, the "we" is a more general usage of the pronoun, not any indication that he himself was doing the entertaining) were "entertaining" or "showing hospitality to" the people in the hotel lounge. The man they are speaking of is being stated to be "about the biggest and loudest" as in "almost the biggest and loudest" or "just about the biggest and loudest", with the "about" being used in the sense of a qualifier indicating that there might be more extreme cases, but this person is close to being the worst (or, in other sentences, the best) example.

And "put in a claim for" is being used to indicate that Father Brown believes that "reverend brother Pryce-Jones" is a better case for being "a pig-headed idiot with one idea". His "claim" is the statement that said Prohibitionist is more pig-headed than "all the fakirs in Asia" and would be thus as likely to be the murderer under that reasoning of fanaticism.

Answer 2

In the above excerpt, "about" is not directly connected to the verb "entertain", so it does not work like, e.g. "talk about". The structure is as follows:

• "we had the honour of entertaining ..."
  • Where? "in this bar-parlour"
  • When? "yesterday"
  • Whom? "about the biggest and loudest and most fat-headed fanatic in the modern world".

The meaning of "about" here is "nearly" or "approximately" (as in "The castle is about three-quarters of a mile away").