That's kind of thing - while playing, it genuinely does appear "pixel perfect" but it's obvious that there is something going on with the way its displayed when you look closely. I can't tell if it's the result of the scale or something with the way the artwork was created. I kinda feel like the checkerboard thing is intentional shading. Many other elements of the image look completely sharp.
It's not shading. It's the result of - as I mentioned - the image being slightly stretched horizontally. I'll illustrate with that "raw video" shot you posted on a previous page.
Say the game runs at 1920x1080. The "240p" equivalent would be 427x240. Actually, that's not quite true - it's 426.6667 (2/3, in other words), but you can't have 2/3 of a pixel. This is your shot shrunken nearest neighbor to 427x240.
Looks pretty pixely! But it's not perfect. You can see slight interpolation in Sonic's eyes and the checkerboard pattern, because 427x240 is not the native resolution of the game. The native resolution is 424x240, as shown here:
Perfect pixels, no interpolation. But it's ever so slightly less wide than 16:9, so you can't scale it to 16:9 resolutions like 1920x1080 or 3840x2160 without some slight artifacts.