What goes through your head can be roughly defined as remembering, or imagining, or symbol manipulating. Imagining includes "imaging" which is just viewing pictures in your head. And remembering covers all aspects of memory - which can include remembering sense experiences, or remembering previous sessions of imagining (including imaging), or rememberings previous sessions of symbol manipulation.
For the author to go on at length to say -- hey, other stuff happens in your head besides symbol manipulation (which includes language) is rather obvious. But he then asserts that much thinking does not involve symbol manipulation. Now, of the 3 categories identified, one can admit that imagining is also thinking, and it may not involve symbol manipulation. Thus I can visually rearrange the furniture in my living room, or visualize a painting before I create it; and I will concede this is "thought". But to then assert as this author does that all thinking occurs without language is rather a step. For often much of my personal thinking is along the lines of "if I do this, then will that happen? And if so, and I do this other thing, will that follow? Okay, lets try this strategy..." etc.
To state that this thinking does not involve language is merely to push it up a level and say that something is happening in the brain (or somewhere) before putting together these logic strings. And of course in the brain we are talking about some kind of neuronic functioning which happens before these verbal thought strings get created. But to assert I could rationally analyze some logical alternatives without using symbols (language) is unproved. Try to do a math problem without "language" (for mathematics is expressed in language.)