The schwa deletion only happens with the first word (américaine) and affects its final e.

There is no schwa in the remaining words.

We could represent the deep phonology of américaine as /a.me.ʁi.kɛ.nə/, the final vowel being a schwa. However, in so-called Standard French, this final /ə/ is dropped in most contexts in words that end with a consonant + ‹e›. This includes masculine/feminine alternations such as américain~américaine. The result is a closed final syllable on the /ɛ/ : /a.me.ʁi.kɛn/.

The deletion of this schwa is addressed in part by Stéphane’s answer here. It’s essentially the same process that, since the Vulgar Latin stage, has been eroding the ends of French words towards the hard boundary of the final stressed syllable.

Incidentally, the clause about “given the deletion of this schwa” is not related to the location of the stress; Walker seems to be simply clarifying the transcription he offers next. I say that because even in dialects or contexts where the /ə/ is realized, it doesn’t typically receive stress: /a.me.ʁi.kɛ.nə/. (One exception is when stress is secondary to musical phrasing, as in « J’ai quitté mon île » where the /ə/ falls on the tonic.)

Good book choice, by the way. It guided some of my undergraduate work in French linguistics.