I see what’s happening now. It’s a difference between NTSC and PAL.
Take this with a grain of salt since it’s from Wikipedia (which has failed badly at documenting video standards in past years), but Wikipedia’s pages for NTSC and PAL show that NTSC has 227.5 color carrier cycles per line, while PAL has 283.75 color carrier cycles per line. (Note: 283.75 is stated explicitly, but 227.5 comes from dividing the color frequency by the line frequency.)
In NTSC, the .5 at the end of 227.5 is what causes the phase to turn 180 degrees each line, resulting in a checkerboard. PAL has 283.75 instead, which causes diagonal lines, not a checkerboard. The video of the Colecovision shows that these diagonal lines are scrolling to the right, even in non-interlaced video, unlike NTSC where the checkerboard only scrolls upwards in interlaced video.
About that. On your video of the Amiga, the white line under the words “Easy Living” has dots scrolling on it. That’s probably caused by comb-filtering in the CRT. (Edit: I realized what you meant by posting that screenshot. The cause probably isn’t a comb filter, then.)
On the other hand, the fact that your ColecoVision is scrolling right, while the Amiga is scrolling to the left, must be caused by the ColoecoVision and the Amiga somehow. The console is what determines the color carrier’s offsets and rate.
I want to make one last note here that the games Battletoads and Battletoads Double Dragon on NES (while you’re playing a level) in NTSC has a similar scrolling diagonal line pattern, but it’s a 1/3 offset instead of 1/4.