I questioned the use of this word a couple months ago, when it was used to describe a young boy.
I am unable to grasp its meaning here:
"In fact, a couple of very good
country agencies happening to come up to town, at the same
time, an agreeable little party had been got together to meet them,
comprising Mr. Snicks, the Life Office Secretary, Mr. Prosee, the
eminent counsel, three solicitors, one commissioner of bankrupts,
a special pleader from the Temple, a small-eyed peremptory
young gentleman, his pupil, who had written a lively book about
the law of demises, with a vast quantity of marginal notes and
references; and several other eminent and distinguished personages."

peremptory [pə'rɛmptərý]
adjective
1 urgent or commanding
example: a peremptory ring on the bell

2 not able to be remitted or debated; decisive

3 positive or assured in speech, manner, etc.; dogmatic

4 (Law) a admitting of no denial or contradiction; precluding debate
b obligatory rather than permissive

[ETYMOLOGY: 16th Century: from Anglo-Norman peremptorie, from Latin peremptorius decisive, from perimere to take away completely, from per- (intensive) + emere to take]
per'emptorily adverb(ial)
per'emptoriness noun

Your definition no. 3 would seem a very plausible candidate.

Bingley

And here are the definitions I liked from MW, wwh. I remember well that discussion here on AWAD:

3 a : characterized by often imperious or arrogant self-assurance <how insolent of late he is become, how proud, how peremptory -- Shakespeare> b : indicative of a peremptory attitude or nature : HAUGHTY <a peremptory tone> <peremptory disregard of an objection>

I would assume def. 3 is the one but it doesn't sound like a particularly pleasant little party to me.

Dear WW: I remember it too. But dictionaries online were not so easy to find then, particularly ones that gave obsolete definitions. Wonderful how new resources keep appearing. Just the other day I found a new and better source for French words. Also there is now a lot more German things. Actually that usage of "peremptory" is a sort of crypto-ellipsis: it only makes sense if you mentally supply the word "manner" or some similar word.