I think it depends on where it gets added. The one on the top and sides of walls would definitely be possible to at least approximate on a PS1, by first drawing the background, then drawing the walls several times with different offsets and different colours, drawing the correct colour last. The tops of the trees seem to have more polygons, so drawing those multiple times in different colours might be slower, but if the game is well optimized it should be able to split the trees in parts and only draw some of them multiple times. And the chromatic aberration on things that aren’t right in front of the sky seem less likely although it could probably be done. I think it’s not that it wasn’t possible to approximate chromatic aberration on 32-bit hardware but more that doing so required drawing the same triangles more times and developers preferred to draw more different triangles rather than the same multiple times. It would at least be easier than depth-of-field blur, which sorta requires semi-transparency, which was slow to do on the PS1.
And one place where chromatic aberration was definitely possible in the nineties and would have looked well would have been in prerendered cutscenes. Those usually had JPEG-like compression artifacts, such as ringing artifacts and chroma subsampling (the latter sorta looks like chromatic aberration). I think if I see something offline-rendered I can’t really see how long ago it was rendered, since that was already very realistic in the nineties.
I also notice that the floor seems to be divided into parts and the ones further away seem to get drawn untextured, kinda like in Spyro.