I wrote to the author who told me simply it means "Speak Cree".
The following is my tiny amount of understanding of Cree from Wikipedia pages and other online resources.
- Nihithawak means the Cree people, in th-dialect Cree (ref)
- Nihithawan means "Speak Cree", in th-dialect Cree (author email)
Woods Cree is Nīhithawīwin, ᓀᐦᐃᖬᐍᐏᐣ in Woods Cree. (ref)
According to wikipedia: Cree is syllabic and highly inflected, and comes in a number of dialects, including "th-dialect" and "y-dialect" (ref). Only Woods Cree has th (written as y syllables modified with a crossbar) and also e has merged with i.
So Woods Cree Nihitha- might be Nehiya- in other forms of Cree.
A Cree dictionary gives some support to this:
- nehiyawak ᓀᐦᐃᔭᐊᐧᐠ NA the Cree people (EC)
- nehiyawewin ᓀᐦᐃᔭᐁᐧᐃᐧᐣ N The Cree language. (MD)
The inflections of Cree include prefixes, infixes, suffixes and can be compound. The dictionary gives two which illustrate the complexity.
- nehiyawe ᓀᐦᐃᔭᐁᐧ VC Speak Cree. (MD)
- nêhiyawêmototawêw ᓀᐦᐃᔭᐁᐧᒧᑐᑕᐁᐧᐤ VTA s/he speak Cree to s.o. (CW)
This entire question is probably better suited to Linguistics SE