Agreed, it's really cool :). A lot of this is very new -- it's only been in the past decade and a half or so that we've been able to record from large populations of neurons (on the order of hundreds and up, see [0]). But there are a lot of smart people working on figuring out how to make sense of this data, and why we see low-dimensional signals in these population recordings. Here are some good reviews on the subject: [1], [2], [3], [4], and [5].
I'm curious about how much of this apparent low dimensionality is explained by (1) the physical proximity of the neurons being recorded, (2) poverty of the stimuli (just 4 sequences in this paper, if I'm not mistaken)
Both good questions. It could very well be that low dimensionality is simply a byproduct of the fact that neuroscientists train animals on such simple (i.e., low-dimensional) tasks. This paper argues that [0]. As for your first point, it is known that auditory cortex exhibits tonotopy, such that nearby neurons in auditory cortex respond to similar frequencies. But much of cortex doesn't really exhibit this kind of simple organization. Regardless, technological advancements are making it easier for us to record from large populations of neurons (as well as track behavior in 3D) while animals freely move in more naturalistic environments. I think these kinds of experiments will make it clearer whether low-dimensional dynamics are a byproduct of simple task designs.