I think it's much more than that. It's also scanlines, and more generally how a pixel looks when it's represented by electrons hitting the phosphor through a shadow mask. Even when a shadow mask is made up of holes, not slits (Trinitron), those holes do not correspond to pixels. This, the particular characteristics of the phosphor, and the fact that the phosphor is behind glass, probably all add up to a very certain look.
By the way, there definitely were "perfect rectangle" (I assume you don't actually mean "square", but rather just non-curved) CRTs later on, or at least very nearly so.
But yeah, maybe I should try the project you've linked, it may really be a good simulation of it. (Though I wouldn't want to use it as my "regular" terminal.)