I don't know shit about neurology, but I know something about pattern matching. Determining amount without counting is probably pure pattern matching.
You see a continuous blob in your vision, and there's a learned neural pathway somewhere that signals "blob -> object". Similarly, when you see several blobs, there's probably a pathway from your eyeballs that connects the neural structure in your mind that represents a number. So you see four blobs, and your mind immediately evokes "4" without thinking.
And I imagine you could extrapolate that to counting rows and columns as well. Unconscious multiplication, simply because seeing certain visual patterns immediately sends a signal to a part of your brain that holds certain numbers.
t. bullshit expert
At least, those are my observations from lifetime of playing video games, learning the game to the point where some blurry pixels in the corner of my vision activate a complex sequence of responses that would be impossible to do consciously that quickly. ("blurry group of pixels - flick hand towards it -> click -> headshot").
So, no conscious thought involved, pure pavlovian learned reflexes.