Your results are normal, because your input size is not an exact multiple of your output size – it is not an exact downscale like 3-to-1 but more like 2.85(ish)-to-1; so eventually there will be output pixels that only correspond to e.g. 2 or 4 or 3½ input pixels and have to be stretched or compressed.
The provided image seems to have 3×3 "large pixels" (dots? cells? squares? I don't know of a good term), so if you claim the original was 480×270, this means it was actually upscaled to 1440×810 and then cropped to fit 1366×768. So the recoverable original is only 456×256.
(To see this visually, open the file in GIMP, select "Enable grid", "Configure grid", choose 3×3px. Note that vertically it doesn't even have an integer amount of "large pixels"; the leftmost and rightmost columns are only 2px wide and cause everything to be offset from the grid.)
So what you'd need to do is:
Pad or crop the image so that both dimensions are multiples of 3 (the "large pixel" size). The vertical size is already good, but horizontally you must pad by 1px left & right – this will also realign the columns to grid. I used GIMP's "Canvas Size" because I don't know ffmpeg filters.
Scale down to 456:256 or 456:-1 because that's the actual data you've got – the rest had been cropped away. I used your ffmpeg command for this.
Here's the result: