For this question, I think a verbatim quote (with context) from the textbook would be really useful in understanding the author's intent.
Edit: Now that it has been provided by Tommy - I guess not really. The author mentions how it would be inappropriate to use it to refer to a third person, but I disagree that it "cannot be used as a question" when referring to the second person. A google search for "うと思いますか" gives quite a few hits (学外実習アンケート集計, 「野菜の摂取や身体活動に関する意識」について (Tokyo Metropolitan Government), 食に関する意識調査), many of which are from questionnaires. The textbook being from 1986 might have something to do with it.
"~うと思うか" does sound like it makes sense, but there are definitely more clear ways of expressing what you probably intend to say when you use that phrasing.
If we take the example "読もうと思うか", are you asking:
- if the listener is going to read the book? (読むか)
- if the listener wants to read the book? (読みたいか)
- if the listener thinks that they might want to read the book?
To me, "読もうと思うか" sounds like number 3 more than the others.