Sorry, but if everything is intelligent then why is a word for it even needed like it is used today - stating that intelligence is an intrinsic property of matter, moves the discussion quite a bit, I think, as it changes what we denote there.
Unlike "artery" which certainly isn't every blood vessel or "yellow" that isn't every color.
"Intelligence" = vessel or color in your example
There are words that distinguish between types/degrees of intelligence. Basal/proto intelligence applies to cells and bacteria. Somatic intelligence is a level higher at tissue. Superintelligence you've no doubt heard of.
It's true that "intelligence" is general/umbrella and doesn't have much meaning, but more specific terms do exist.
Most human societies claim dominance over “everything else” aka “nature” and in order to do that you need a reason “humans” are different from “nature”
I'll highlight the gp's point here because it is subtle but important
and I'll add one more point: there's a difference in how people speak colloquially and how words are used by experts. In fact, different groups of experts may use the same word to mean different things (e.g. a mathematician and mechanic both call things "manifolds", yet you shouldn't confuse them). Natural language is highly overloaded (which is a big reason we invented formal languages).A problem with the word "intelligent" is that very few people look to see how it is actually used in different fields like neuroscience, psychology, or machine learning, which all use the word a bit differently, and none of them use it in the way that we use in natural speech.
But I can ask you how "yellow" is the color green. It is certainly some yellow. Definitely more yellow than red is. Even more so, we might argue over if black is more yellow than white or not. Which in some settings black is more yellow than white and in other settings white is more yellow than black. Hell, the fact that you can read this and understand it is clear evidence of both utility and ambiguity. We haven't even mentioned that people may use the same definition but use a word to mark a certain threshold and disagree on that threshold (the root of so many painful to watch arguments).Everything is just a bit fuzzier than you think.