I imagine most people will have differeing opinions on the complexity, but assuming there are only three levels, I kinda agree. I would call wizard High and I think Ranger is teetering on Low, but otherwise think this correct.
As a DM who has mostly played with beginners including children since 5e, I think I understand a thing or two about 'complexity'.
In the context of a RPG, you can say that complexity is in general about the need for making choices. Things that increase complexity are: the more frequently you have to make a choice, the larger number of options to choose from, the more aspects (costs and benefits) need to be considered in the choice.
But first of all, build complexity and play complexity are not the same thing, they are correlated but definitely not the same. An easy example on this is Sorcerer vs Wizard (5e versions). Consider just the selection of known spells, more or less the number of options (at build) are the same, but the Sorcerer knows very few spells and doesn't have the open-ended option of adding more spells from scrolls, therefore the build complexity of a Sorcerer is higher than Wizard for the sole reason that you cannot afford many mistakes in your spells choice, while you can be more relaxed with a Wizard. But once you start playing the game, the Sorcerer's spells are what they are while the Wizard has more choices to make in which spells to prepare each day, which increases its play complexity. [This example does not consider other abilities of Sorcerers and Wizards, like metamagic or arcane recovery]
I think it's important to acknowledge these are two different complexities, and that having a class that allows a quick and easy build to start playing immediately, doesn't necessarily mean playing it will be easy.
Second, don't mix up the mechanics with the narrative. I am pretty sure that WotC's table is about class mechanics (probably more about play complexity than build complexity, or a mix of the two). The narrative is up to the player's roleplay style. I am saying this because someone may be deceived by thinking "barbarians are dumb so they must be low complexity" or "a wizard is a genius so they can never be too low complexity".
As I don't know the 2024 versions of the classes, I have no idea how appropriate those presumed complexity levels are...
I can presume that they rated the Sorcerer's complexity higher than Wizard primarily because the Sorcerer has an additional limited resource pool to manage (the sorcery points).
I don't think the original 5e Rogue was really low complexity, mainly for two reasons: sneak attack required at least some attention in combat to make sure you enable the bonus, and generally the Rogue's features increased the importance of using your movement around the battlefield compared to others. But I also know that since Tasha, WotC has added more ways for Rogues to enable Sneak Attack, to the point that it might even handwave all requirements by now and make it always on, and that certainly would make it easier to play.
Finally, I am a bit skeptic that Paladin is only average complexity, the 5e version had enough resource-based mechanics to make it high complexity between spells, channel divinity and lay on hands... plus auras that required to keep track of your distance from allies, and smites which being bonus spells that boost attacks also IMO carry on a small complexity increase. But again, I don't know what they've done with it in the 2024 version.