Re: "superintelligence" is undefined
Personally, I think we "know [intelligence] when we see it" precisely because we are it (and assume it is the same for other humans). Thus we have a tendency to judge any "intelligence" against our own, because that's all we know. We do recognise "intelligence" at some level in other creatures (other primates, dolphins, corvids, octopuses, …) but struggle to categorise it. Octopus intelligence, to take an example, must be wildly different to our own (they have a central brain, but also a brain in each tentacle, and evolved in a very different environment to us). We cannot imagine how an octopus "thinks" – and yet, even in octopuses, we recognise something akin to the familiar human form of intelligence. (Well, we think we do, but to what extent is that just anthropomorphising?)
Interestingly, as regards AI, people (especially in Reg forums!) appear to set the bar higher than human intelligence. AI systems are criticised for making mistakes, making stuff up, failing to solve some problem, etc., etc. – and yet of course humans do these things too. (I am invariably heavily downvoted on these forums for pointing this out. I'm not sure why.) My view is that this is in any case the wrong question to ask about AI (or any technology, for that matter): not how "smart" it is, but how useful it is to us (here, under "useful", I include "not draining the planet's resources to an obscene degree").
> We have rather severe limits in the amounts of information our little brains can handle …
I think our limits are perhaps further out than you give credit for: consider the amount of knowledge, know-how and experience accumulated in an adult human. Our storage capacity and connectivity is hardly to be sneezed at: roughly 85 billion neurons in the human brain (about 15 billion of those in the cerebral cortex), and in the region of 100 to 1,000 trillion synapses (a neuron may have thousands of synapses). That dwarfs modern computing technologies (and the brain is also orders of magnitude more energy-efficient than current technologies). We know pitifully little of the organisational principles, honed by evolution, that underpin information processing in the human brain (this is close to my area of research), but it is certainly orders of magnitude more sophisticated (in some sense) than current AI.
As a passing remark, current AI is frequently derided as "just" statistical association. In fact there is increasing evidence that information processing in brains actually has a strong statistical component. This should be unsurprising: in a world overwhelmingly rich in rapidly changing information, statistical modelling is a practical way to cut through the noise and home in on the information that is relevant to the task at hand. It should not be surprising that evolution will have exploited this. Think of driving a car: your sensory apparatus is delivering an incredibly rich live-stream of dynamically-changing information. You cannot process all that information in real time, and you don't have to – you need to distil that stream into something your brain can handle in real time, and that is actually relevant to driving safely. With some training, your brain does this magnificently well (current self-driving technologies… not so much!)