Does Oxygen-burning process produce Neon?
The pages you’re looking at describe fusion of two similar nuclei with each other (e.g. oxygen with oxygen).  But fusion doesn’t have to involve identical nuclei, and reactions involving more abundant nuclei will in general occur at a higher rate (though this can vary based on other factors, too).
Long before oxygen-oxygen or neon-neon reactions become important, reactions involving helium nuclei (also called “alpha particles”) take place.  That is what the text in your book is referring to: C + He gives O, and O + He gives Ne. See the list in this Wikipedia article on the alpha process.