I can’t find any explicit copyright licence on the vimtutor text. There’s contact details for the author, but the fact that it mentions “bitnet” suggests the details are very, very old. A web search for “Bob Ware Colorado School of Mines” brings up a likely-looking obituary from 2013, so contacting the author for permission may prove difficult.
It might be worth posting in the Vim subreddit or mailing list or something, just to see if anybody objects, but as a practical concern it’s probably fine to just copy the most relevant parts and acknowledge the source in the beginning “what is this document” section.
The best discussion of tutorial-writing I’ve read suggests that the point of a tutorial is to get the user to that first rush of “I can do this!”. It doesn’t need to be something interesting or useful, it just need to be something complex enough that they can’t do it by accident, and simple enough that they can get there by mechanically following instructions. Documentation about writing plugins and custom modes is definitely needed too, but might be better suited as how-to guides or even explanations rather than tutorials.
While I don’t really have the time or focus to write comprehensive Kakoune documentation at the moment, I occasionally blog about things as I learn them, and it would be great if there were more blog-posts about Kakoune in the world, for people to find via search-engines and the like.