I get what you mean here, but I still think it’s funny because it reads like you’re worried that all the hamsters and hippopotamuses that post on this board would hijack your thread and make it about how we shouldn’t judge mammals’ value by intelligence. And you just know the dolphins who post here would be making a stink too just out of some weird mammal guilt, even though they’re obviously one of the most intelligent mammals.
My guess would be that it’s probably going to be some grazing herbivore since it doesn’t have to outwit anything with its hunting skills and possibly it has enough defenses inherent to its design that again it wouldn’t have to outwit a lot of carnivoires trying to kill it. Plus, as mentioned in the OP, it doesn’t appear to display an overabundance of intelligent behavior so I throw the ‘Rhino’ out there.
Well, if we’re just guessing, how’s the sloth? It doesn’t have to move quickly, so perhaps it doesn’t need much processing power?
Among domestic animals, probably the sheep. As to world wildlife, Peter Hathaway Capstick, who wrote extensively about African big game declared that the rhinoceros was far & away the dimmest bulb among the large herbivores.
Not to rain on your parade, but I have confidence that my dog is stupider than yours. My poor mutt is stupid as a box of hair.
When we talk about animal intelligence, one metric often used is “trainability” - the infamous rankings of dog breed intelligence were based on learning a cue in less than five repetitions and obeyed them 95+% of the time.
I’ve personally trained lots of mammals. (Want a list? OK. Horses, cows, sheep, goats, pigs, cats, dogs, rabbits, guinea pigs, opossums, skunks, squirrels, woodchuck, ferrets, hedgehogs, fruit bats.) All these animals have been capable of being trained, e.g., can recognize an event marker (aka bridge, usually clicker or whistle), that the marker is a result of some aspect of their behavior, to accept a primary reinforcer (treat, usually food) and, to actively seek the reinforcer through modifying their behavior. Does that make sense?
Those animals that fulfil the metric from the dog test the best (short time to learn a cue, consistent performance) were dogs and horses - obviously, they’ve been selectively bred for trainability for a long, long time. Other domestic species, like goats, rabbits, even ferrets, I’ve found to be very motivated and relatively easy to train.
The animals I’ve had to work harder to train include sugar gliders and sheep - these are communal living, commonly preyed upon species, with well-developed “flight” reflexes. Does this mean a sugar glider is less intelligent than a hedgehog? No, just less trainable. In some ways, trainers enjoy the challenge of a so-called “dumb” species - it just means we need to work harder to motivate the animal. My dog breed of choice, basenjis, are right at the bottom of the above list… a border collie would just seem too easy!
Since no one else has said it, I will. Homo sapiens. What other mammal knowingly uses up its food sources until they are nearly extinct (bison, cod, blue fin tuna) or poisons its own environment (too many to list) to the point where it can no longer live there? I’m no tree-hugger or PETA member but that seems pretty stupid to me.
What’s that in the universally accepted brain measurement of walnut?
Being too smart is probably more of a reason; after all, if humans were only as intelligent as the other Great Apes, our population and resource usage would probably be similar (several hundred thousand, all in Africa). Of course, the problems you mention are a result of being dumb (as used here, dumb doesn’t mean unintelligent), but most, if not all, animals would do the same if given the opportunity (and that does happen, resulting in population boom/bust cycles).
Sadly, it’s focused exclusively at the top end of the scale, as opposed to the bottom end of the mammalian list. Still, the equations should apply to some extent if we can dig up the relevant data for, say, sugar gliders, hedgehogs, and domestic sheep. (Also, are wild sheep noticeably more intelligent than domestic sheep?)
A little understated: their brain is 0.2% of their body weight. 40% of their skull interior is cerebrospinal fluid. They are kinda like this famous picture.
Nonsense. We eat almost anything, so if we deplete one food source, we’ve got plenty of others. We are the most numerous species of large mammal on the planet, and we are more geographically dispersed than an other large mammal with the possible exception of the other mammals we domesticated. Our extremely large population is growing almost exponentially.
As for polluting the environment so we can no longer liver there-- what percent of the habitable land has that happened to? .00001% Maybe? If that.
Naked mole rats, maybe? Being “eusocial” (hive-like), perhaps individual NMRs do not get taxed with much decision-making, as the superorganism handles a lot of that?
Just about all of them would, given the opportunity, and many have done so when circumstances have allowed. Homo Sapiens, by contrast, is the only species known to be smart enough to realize when it is doing something like this, and to at least consider the possibility of doing something about it.
On the other hand, perhaps homo sapiens is the only species to consistently produce individual dumb enough to think it is clever to suggest that their own species is the dumbest, just because its collective actions do not always reflect ideal rationality.
Or, in other words, there is really no sound basis or metric for comparing intelligence across species boundaries. The concept is really only applicable to comparisons between humans (and, God knows, it is vague and crude enough even there), or, in principle, to beings with whom humans could, potentially, have communication at a level of detail and complexity comparable to that provided by human languages. (If we actually found that dolphins do have a language, and learned how to speak and understand it, only then could we say something meaningful about their intelligence.)
But in absolute terms, a blue whale brain is huge, and it does not really seem to be doing anything very extraordinary with it by way of controlling its body or processing sensory data. It looks as though it ought to have a lot of spare capacity left over for stuff like, say, higher mathematics or whale poetry. 
Well you have to be able to agree on a definition of intelligence that is not just based on seeming human. Do that and it can apply to artificial intelligence too.
I’ve previously proposed: “the ability to solve novel problems of salience to the individual” but have never been able to build a consensus around it.
Whales not doing anything extraordinary with sensory data? You try keeping echolocative tabs on a variety of allies, enemies, and threats in several cubic miles of water volume! That said it doesn’t have fingers to worry about … (again, a big chunk of our cortices devoted to those little things)
What fingers and eyes are to humans, apparently the front teeth are to naked mole rats.
And this is cool: apparently becoming a breeder NMR gives one the opportunity to have more brain cells than those who are non-breeders (subordinants).
Karen Pryor, former head dolphin trainer and curator at Sea Life Park (Oahu, Hawaii) wrote regarding training penguins: (Not exact wording, but fairly close, as best I remember it.)
The rigor and clear presentation of this makes me more likely to accept his conclusions.
I especially like the concept of EQ.
The Xenarthra, formerly known as the edentata (anteaters, armadillos, etc.) have really small and primitive brains. As a group they’re probably the least intelligent living order of Eutherian (“placental”) mammals. Oddly enoug braininess took a while to get established in mammals- the early Cenozoic mammals had far smaller brains than current mammals of similar body size.
A six-banded armadillo called Tonka did pretty well for me, training-wise. He was very food motivated.