It's not that complicated,
imo. :)
TVs of the old analog standard ("SD") draw 525 lines in two passes (even lines and then the odd lines). Each pass is a
field, two of these interlaced fields are a full frame. Fields are drawn at
60/1.001 times per second (less than 60 because the format was extended from b/w to color), i.e. standard NTSC video framerate is 30/1.001 fps.
- "Video" generated in this format (e.g. TV shows) can be deinterlaced with a deinterlacer like QTGMC.
- "Film" converted to this format (24fps movies and anime) can be restored via IVTC (inverse telecine). Avisynth filters useful for that are AnimeIVTC, Decomb and TIVTC.
- Consoles like the SNES usually trick the TV into displaying the fields on top of each other, so the result is 60fps at half the vertical resolution (with black scanlines which the drawn lines bleed into, depending on brightness). Capture cards that expect the signal to be interlaced will put two of these fields into one frame, i.e. it looks like the .gifs you posted. The solution is to simply separate the lines again, e.g. with the Avisynth filter SeparateFields. (I couldn't do that because the original lines were lost due to the resizing.) The correct aspect ratio can be recreated simply via PointResize(Width, Height * 2) (doubling each line) or Spline64Resize(Width / 2, Height) (horizontal shrinking).
If the source was already progressive to begin with (newer consoles, PC) then the interlacing happened somewhere in the capturing/processing.