Wow that is mind-blowing. I could not possibly imagine a world without words, especially the ones in my head. It goes against every intuition I have to believe in thought that lacks language.
For instance, suppose I realize I'm out of milk. It'll come to mind that I should go to a grocery this afternoon to buy more milk, but this intention doesn't form as a complete sentence in my head. It may literally take a couple seconds for me to recall the vocabulary I'll need to express this thought in words, but I can continue thinking about my trip to the grocery -- which one I should go to, what else I need to pick up there, etc. -- before any words have even come to my mind. So ideas and their linguistic representations are very distinct to me, and sometimes I don't even bother with the latter at all, because (for whatever reason) forming the linguistic representation of a though imposes a significant overhead on my brain. (I'm also dyslexic, for what it's worth, and I often wonder of these issues are related.)
My hypothesis is that for people with better functioning language centers than mine, words may come to mind so easily that the delay between thought and linguistic representation is imperceptible to them, hence they "think in words". But for people like me those words might come late or not at all, but regardless, I do think all the same...
(To me, thinking in words seems strange and inefficient. On the other hand, I often have clear and simple thoughts in my head that take me several minutes to translate into any language, because none of the words and expressions I can think of seem just right, so thinking in words seems like it would be useful for communicating.)
I have met other people who share your intuition, but for me (native speaker of English with normal hearing) and for my wife (native speaker of Taiwanese with normal hearing) it is routine to think visually, with no words at all. We have multiple thinking styles, and quite a bit of our thinking does not involve words. I used to have the intuition that everyone can think visually, until I met people who self-report that they cannot imagine doing so.