We are not mere animals.
Look, us humans consistently project our behaviors and maneurisms onto the natural world to see if and how our behavior is present in other beings. This comes with a huge bias, because we, as sentient beings, are aware of what it is we do and why we do it, and thus attempt to give rhyme and reason to what other animals do based on our preconceived notions of behavior.
Basically, animals behave a certain way, and we attempt to characterize as having some correlation to what we do as either natural or unnatural, when it is us that makes that distinction, not the animal.
The thing is that you would probably be the first to say that the conservative people who hold "March of the Penguins" as a testament to the righteousness of monogamy and the heterosexual family unit are batshit insane, that the penguins merely do what they do because that is what they do, and that their monogamous lifestyle for the season does not mean anything to the natural identity of monogamy or other such human behaviors. You may even be the one to say that there are gay penguins... And in that very moment you would understand that these behaviors only come to have a sense of meaning and purpose when human beings come to interpret them within our sentient, reasoned existence.
We need reasons for behavior. That reason is either that it is natural, or that it is nurtured, but it is still a reason. Animals do not have any such need to reason to behavior, nor do they project their actions onto us. They simply react and interact to and with their environment. With us, that interaction and reaction comes with an implicit cause. Hence, sentience.
Now, let's look at your idea of intelligence, based on national geographic, and you might see that a lot of it is useful and or instinctual.
So, they can reason basic math. That's good. It's good to know that one predator is less than three, and that if you take 5 food items from one place and 3 from another, that equals more fish than either place had itself.
They categorize colors and shapes, and identify hundreds of objects. Good. These animals all seem to live in light abounding, varied habitats with hundreds of different plants, animals and colors to keep track of and assess their interactions, such as "purple flower, if eat, kill me".
Those that understand spoken instructions are always trained through pavlovian response of behavior and reward. But I'll get back to this.
Those that are able to see the difference between facial expressions and body language are... good observers. Body language in dogs is very easy to understand. Animals that have to interact with others can see aggression in body language, and facial expressions, such as baring teeth with chimps, also have subtle connotations that we also perceive. This isn't extraordinary behavior in the least, it is a part of their innate ability to read another being and assess how they will react, the danger they present, or otherwise.
The sense of humor bit is a particularly obvious case of anthropomorphizing animal behavior, because a sense of humor implies something that is not necessarily present within the animal. We all know senses of humor within human behavior, but for an animal, this sense of humor is what we think it to be and assimilate it to, not necessarily what is actually happening. Think back to the penguins. When they "cuddle", we see some great form of bond and physical intimacy. But if they're simply learning the other's pheromones, suddenly the magic is lost.
Now, about the training. I volunteer at the Long Marine Lab, one of the world's greatest research facilities on the cognitive ability of marine mammals. We have the world's only captive northern elephant seal, researchers pioneered the training of sea otters, and one of the world's most "intelligent" animals is Rio, a Californian sea lion. Rio was raised in captivity and has undergone extensive learning programs since the beginning, and at 22, is essentially Sea Lion college level. Now, the research they conduct on Rio's ability to remember letters, symbols, associating them, complex instructions and directives, complex grammar issues, all in a language previously foreign, is astounding. What it tells us is that the adaptability and capacity to learn of many animals, like you mentioned, has been extremely underestimated, and we are only now beginning to break the surface on just how complex their interactions are with their environment, with each other, and their ability to learn from new situations. Some will call this intelligence, and intelligence it is, as opposed to something that is incapable of learning.
However, where I differ with you, and what you jump to in your last sentence, is the difference between the ability to learn as intelligence, and sentience and reasoning behind the very fact of learning... It is the difference between learning, and teaching to learn.
The way the dolphins, otters and sea lions are trained is called bridge and target. The bridge is something, like a whistle, or a call, that signals that they have done something correctly, and that food is coming. The target is what they need to touch to get the bridge signal. Now, the training is very complicated from there, but the premise is still the same. You train the animal to respond to various signals with a behavior that will get them a reward. Now, with dolphins, there are instances where they seem to do the behavior for the sole purpose of pleasing their trainers, as they don't necessarily receive a reward. But they are responding to stimuli we have taught them to respond to, they do not intuitively do it once a signal comes, the first time ever. So, their ability to learn from us as we teach them is incredible and amazing. Some would say this adaptability is a testament to a higher creative power. But intelligence that invents, it isn't. These dolphins for example have been trained to jump and touch a ball some 10 feet out of the water. They could easily jump into adjoining pools when they are separated to mess with the trainers. But they don't. Even when the other animal is getting food and we know they're communicating that one has food and the other doesn't. That is because they have not been trained to.
Animal intelligence is associated with the behavior that us humans have in our inquiry as to why we should even do anything at all, and the reasoning behind it, the idea of mortality and our separateness from nature in some degree as ones who change what Nature even means. That animals can reason, in terms of a + b = c, along lines familiar to us makes sense. However animals do not reason like we do when a = b, b = c, thus a = c. We are aware of our actions along lines much deeper then any animal. This is why we continuously try to associate our actions with the natura, to find some reaosn for their very existence.
Just like the octopus who perchance figured out how to open the bottle by trying to get inside the hole in the lid and now knows how to get the crab every time, animals can learn. But it is only when the animal gets the crab and puts a trap for the human, knowing they will inevitably retrieve the bottle, that you could consider it "intelligence" as ours.
