Mexico isnt gonna get anything back (at this point its too American for it to be justifiable and Mexico is going to be too weak after having thrown out Maxxyboy to annex anything).
While the map is certainly ASB, and a lot of that is either too American, or territory that neither Mexico nor the CSA actually ever held, I can see a Mexico that is gotten its shit together beat the CSA in a war and gain some territory - it would however not be nearly as much as this.
But Mexico gaining the Nueces Strip and the trans-Pecos strip isn't difficult to see. The Nueces Strip had a good Mexican population, and trans-Pecos was very lightly populated at this time.
As a result Texas - the only state that looses territory - is likely to split off the CSA at this point (plus if the war is in the early 1900s it already has its oil revenue and will likely be looking for a way out anyway).
If the CSA also happened to have its Arizona claim (the Southern half of New Mexico and Arizona) it would likely end up in Mexican hands as well, since it probably wasn't of much use to the CSA, the territory would be rendered useless even further without El Paso, and the US would be happy to see the CSA further away from the Pacific.
Mexico wouldn't have to march into the CSA, blockade New Orleans, and occupy Richmond (all impossible) for this to happen. All it has to do is move into these territories and hold on to them until the CSA implodes from within via Texas splitting off, a slave revolt, and possibly US intervention.
The US getting the whole rest of the CSA back seems unlikely to me, by now it is likely better to have a friendly/puppet government running the place and get significant trade benefits out of this. The US would get a lot more in the short run, with a lot less investment. If the USA also joined the war on Mexico's side, rest assured the CSA would be curbed stomped and the US might re-admit some border states/territories if they swear loyalty.