note: based on comments below it's clear now that there are several problems, so this is currently a partial answer.
I think I have it (at least partly) figured out.
But one problem with the current plots, but there is still a bug in your analysis because Earth's analemma as defined in your link should range between +/- 23.4 degrees and yours goes from -24 to -69, which has about the right range but is centered on about -46 degrees.
You haven't explained what you've done so it's impossible to debug it in an answer, but that's not declination. However it might be the elevation of the sun at midnight (rather than noon) from mid latitude!
The vertical axis of the analemma as defined in your link for each planet should be generated from the observed "declination" of the Sun based on each planet's axis. Horizons is giving you RA and DEC of the Sun using the standard Earth-based coordinates à la J2000.0 no matter from which planet you are observing it from.
If you go back and look at Mercury's analemma on your linked site you'll see that it only extends +/- 0.035 degrees which is the tiny angle between Mercury's orbital plane and its equator.
I'll bet that if you define a topocentric location on each planet at it's north pole and use the apparent elevation of the Sun above the horizon, you will get better looking plots. Try it for Earth first, it should make the familiar analemma pattern extending +/- 23.4 degrees above/below the horizon.
There are answers either here or in Astronomy SE explaining how to get alt/az from a topocentric location on another planet from Horizons. I'll look for some but I don't think it will be too hard to find.
- topocentric alt/az from the Moon: https://space.stackexchange.com/a/37155
- not quite topocentric but potentially helpful: https://space.stackexchange.com/a/25357