My theory: The article mentioned an earlier prototype used 384×256, a 3:2 ratio. 512×342 is the even height that gives closest to a 3:2 ratio with a pixel width of 512.
adjust the width control until the raster is 7 inches (177.8 mm) wide
adjust the height control until the raster is 4.7 inches (119.4 mm) high
This gives a physical aspect ratio of 1.489...:1, while the pixel ratio is 1.497...:1 (0.5% off square)
It makes a pixel 1/73.14...inch wide and 1/72.77in tall
Still, as a sibling comment points out: Once you decide you can hit your screen redraw time with around 170,000 pixels on the screen, that you will use a 9" 3:2 CRT, that you want one pixel to be close to one printer's point (1/72 inch), and that your framebuffer needs to be oriented around 16-bit or maybe 32-bit quantities, you aren't left with a lot of options. 480 pixels is not quite enough to show the width of a standard US letter page with 1/2 inch left and right margins, 512 pixels is (and can even fit a scroll bar)
Note: I don't have any evidence that the choice of a 9" screen or a 3:2 ratio preceded the choice of pixel resolution, it could have happened the other way around.
Also blowing a hole in one leg of my argument: MacWrite 1.0, as screenshotted at https://lowendmac.com/2006/macwrite-1-defining-word-processi..., used 80 pixels per inch for the onscreen ruler, not 72! With this scale, 7 inches (US letter paper with 1" left and right margins) plus a scrollbar fits in 512 pixels.
The pixel resolution is 512x342. The Macintosh Service Source https://www.macdat.net/files/pdf/apple/servicesource/macinto... page 76 says to do the following:
adjust the width control until the raster is 7 inches (177.8 mm) wide
adjust the height control until the raster is 4.7 inches (119.4 mm) high
This gives a physical aspect ratio of 1.489...:1, while the pixel ratio is 1.497...:1 (0.5% off square)
It makes a pixel 1/73.14...inch wide and 1/72.77in tall
Still, as a sibling comment points out: Once you decide you can hit your screen redraw time with around 170,000 pixels on the screen, that you will use a 9" 3:2 CRT, that you want one pixel to be close to one printer's point (1/72 inch), and that your framebuffer needs to be oriented around 16-bit or maybe 32-bit quantities, you aren't left with a lot of options. 480 pixels is not quite enough to show the width of a standard US letter page with 1/2 inch left and right margins, 512 pixels is (and can even fit a scroll bar)
Note: I don't have any evidence that the choice of a 9" screen or a 3:2 ratio preceded the choice of pixel resolution, it could have happened the other way around.
Also blowing a hole in one leg of my argument: MacWrite 1.0, as screenshotted at https://lowendmac.com/2006/macwrite-1-defining-word-processi..., used 80 pixels per inch for the onscreen ruler, not 72! With this scale, 7 inches (US letter paper with 1" left and right margins) plus a scrollbar fits in 512 pixels.