The evidence doesn't support as close a relationship between dreaming and REM sleep as the authors suggest. See:
Solms. 2000. Dreaming and REM sleep are controlled by different brain mechanisms. BEHAVIORAL AND BRAIN SCIENCES (2000) 23, 793–1121.
https://neuro.bstu.by/ai/To-dom/My_research/Papers-2.1-done/...
»It is generally accepted that NREM mentation that is indistiguishable from REM dreaming does indeed occur. Monroe et al.’s (1965) widely cited study suggests that approximately 10–30% of NREM dreams are indistinguishable from REM dreams (Recht-schaffen 1973). Even Hobson accepts that 5–10% of
NREM dream reports are “indistinguishable by any criterion from those obtained from post-REM awakenings”
(Hobson 1988b, p. 143). If we adjust this conservative fig-
ure to account for the fact that NREM sleep occupies ap-
proximately 75% of total sleep time, this implies that
roughly one quarter of all REM-like dreams occur outside
of REM sleep.«
A recent reference that discusses this is:
Nicholas and Ruby. 2020. Dreams, Sleep, and Psychotropic Drugs. Front Neurol. 2020; 11: 507495.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7674595/
»Regarding the link between dreaming and neurophysiology, 60 years of debates has been necessary to get rid of the rapid eye movement (REM) sleep hypothesis of dreaming, and it is now acknowledged by a majority of dream researchers, be they neuroscientist or not, that REM sleep is neither necessary nor sufficient to get a dream report and that dream reports can be obtained at the awakening of any sleep stage (2, 7, 9–12). It is also now clear that the complexity and story-like characteristics of dream reports are related to sleep stages but also, and even more so, to circadian rhythms leading to more vivid and complex dreams in the morning than in the early night [e.g., (13–15)].«