The word isn't found by Onelook, but it suggests some others.
Searching Google for the sentence without testotum gives some alternate words.
My rod creaked and bent double,” a stout, red-faced gentleman was saying, “and the birch spun like a tee-totum.
"My rod creaked and bent double," a stout, red-faced gentleman was saying, "and the birch spun like a teetotum.
A teetotum is:
A top, usually having four lettered sides, that is used to play various games of chance.
Images from Wikipedia:
It may be worth noting that teetotum isn't a well known word; at least I hadn't heard it before.
Project Gutenberg texts are scanned from books. Sometimes there can be mistakes with the OCR (optical character recognition), the computer program that guesses the letters, especially in older books with less clear type. Humans volunteers proof-read the text before release, but some mistakes can slip through, such as this one.