***** NOT A TEACHER
***** ONLY MY OPINION
I think that the problem may lie in your definition of the word
"archaic." Usually, a book that was written "only" a hundred
years ago is not considered "archaic." I admit that I know
very little about Mr. London's writings, but I have heard that
it was vigorous and effective. In other words, if you wrote the
way he wrote, most people would praise your writing. (Of course,
a few things have changed in the last 100 years in vocabulary, but
I imagine that the grammar would mostly reflect current grammar.)
Of course, if you wrote the way Shakespeare wrote, then we would
call that "archaic," and many people would have difficulty in understanding
what you were writing.
Hopefully, someone who is a fan of Jack London's novels will answer
you. I am very eager to know something about Mr. London's grammar.