It looks like Benadryl and other sedating antihistamines count as sleeping pills. The interviewee Walker appears to be referring to a passage from the book he wrote (mentioned in another comment I wrote in this thread), which references a study called "Effectiveness of non-benzodiazepine hypnotics in treatment of adult insomnia: meta-analysis of data submitted to the Food and Drug Administration." [0]

According to Encyclopedia Britannica, non-benzodiazepine hypnotics include antihistamines: "Hypnotic agents (nonbenzodiazepines) include chloral hydrate, some sedating antidepressants, and sedating antihistamines, such as diphenhydramine (Benadryl) and hydroxyzine (Atarax)." [1]

[0] https://www.bmj.com/content/345/bmj.e8343

[1] https://www.britannica.com/science/nonbenzodiazepine-drug