I doubt that this is different for other people. I believe that those people who claim that they never think using language are never thinking about the abstract or remote things about which I think using language.
For instance, I can think about a model of CPU without naming it, if it has been included in some of the many computers that I have used during the years, by recalling an image of the computer, or of its motherboard, or of the CPU package, or recalling some experiences when running programs on that computer, how slow or how responsive that felt, and so on.
I cannot think about a CPU that I have never used, e.g. Intel 11900K, without naming it.
Similarly, I can think without language about the planet Jupiter, which I have seen directly many times, or even about the planet Neptune, which I have never seen with my eyes, but I have seen in photographs, but I cannot think otherwise than with words about some celestial bodies that I have never seen.
The same for verbs, some verbs name actions about which I can think by recalling images or sounds or smells or tactile feelings that correspond with typical results of those actions. Other verbs are too abstract, so I can think about the corresponding action only using the word that names it.
For some abstract concepts, one could imagine a sequence of images, sounds etc. that would suggest them, but that would be like a pantomime puzzle and it would be a too slow way of thinking.
I can look at a wood plank thrown over a precipice and I can conclude that it may be safe to walk on it without language, but if I were to design a bridge guaranteed to resist to the weight of some trucks passing on it, I could not do that design without thinking with language.
Therefore I believe that language is absolutely essential for complex abstract thinking, even if there are alternative ways of thinking that may be sufficient even most of the time for some people.