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.)
The hercules card had a "80 × 25 text mode with 9 × 14 pixel font (effective resolution of 720 × 350, MDA-compatible)" (wikipedia), but the graphics mode was 720 x 348.
It always blew my mind that you'd buy a new videocard, and plug the big CRT monitor in it, and it would switch between different resolutions. Precisely because the holes and pixels don't line up, they supported a huge range of resolutions and it didn't look as smeared as on LCDs.
I think the mask in the CRT itself also contributed to a kind of subpixel Anti-Aliasing.
I don't know about older hardware because I started in the early '90s, but the VGA didn't have scanlines the way game consoles played on TVs had. The VGA had a built-in line doubler, and the minimum horizontal scan rate was 31 kHz. In fact, very few computer monitors at that time supported 15 kHz.
CRT image is an analog signal so it always has those little imperfections, especially as the screen ages and phosphor matrix gets burned, and there's dust settling so all dissipation curves change slightly, and each analog electronic component on the board had it's own tolerances that changed over time, and then EM noise from environment and power grid was also leaking - all of that slightly affected timing and precision of the beam. It's not just that it's super hard to digitally emulate that, but even back then no 2 CRTs were giving 100% the same image, especially after a few years of being in use.
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.)