Not to dismiss the thought that's been put into this, but the aspect ratio of the image (display aspect ratio) is almost always the wrong way to approach this. Retro computers typically have a limited number of dot clocks and video timings compared to the frame sizes that they can support. The Atari 8-bit, for example, supports only a single pair of horizontal and vertical refresh timings, but is very flexible regarding how wide and tall the display is. If you try to estimate aspect ratios based on the image area, you'll get lots of variance because many games deviate from the 320x192 area that the operating system uses.

On top of that, it's a mistake to assume that the original images had squares. With a small number of pixels per tile and both an aesthetic and efficiency requirement for the tiles to be uniform, it's highly likely that what look like squares actually weren't -- they could only get so close with the available resolution. I see a lot of people try to guess aspect ratios based on what they think the art was intended to look like, and on multiple occasions have had to boot games on original hardware and contemporary displays to prove that, no, what looked like a circle was actually slightly elliptical.

The correct way to approach this is by starting from the pixel dot clock and video timings to determine pixel aspect ratio and work backward to display aspect ratio. This also reveals another typical sign that aspect ratios are being determined wrong -- when significantly different pixel aspect ratios are determined for multiple systems that all supported NTSC artifacting colors, like the Apple II and the Atari. Supporting NTSC artifacting means NTSC-compatible timings and a dot clock that is an integer multiple of the color subcarrier, which means similar pixel aspect ratios.