The tutorial article is much easier to follow, yes. Now, it's been years since I did anything with Pauli spinors, and one reason for that is that they rather turned me off theory; I could never understand what they were supposed to represent physically. This idea of seeing them as a matrix expression isomorphic to a geometric relation is appealing. Still, I couldn't get to the point of visualising what the various operations were doing; I understand that you're keeping track of objects having both scalar and vector components, but I couldn't quite see what was going on as I can with cross products. That said, it took me a while to learn that trick for cross products, so quite possibly it's just a question of practice.