I think the designer(s) of the chart were trying to coin a term with a broader applicability than “logical fallacy”, and used an (awkward) variation on “rhetorical” to try to key up the idea that the chart covers bogus argument forms that are rhetorically sneaky but that don’t necessarily contain a logical fallacy. However, if that’s what they were trying to do, I don’t think they succeeded (and maybe i’m giving them too much credit by assuming they were trying to accomplish such a thing).
And, in any event, I think “rhetorical” (let alone “rhetological") and “fallacy” make for an awkward fit: I know just enough about formal logic to be dangerous, but ISTM that an argument that is valid in form but presented in a sneaky, manipulative, or otherwise underhanded manner (i.e., wih a rhetorical sleight of hand if some sort) doesn’t really contain a “fallacy”: the problem is that it is weaselish, not that it is fallacious. OTOH, an argument that is invalid in form almost certainly (certainly?) does contain a logical fallacy. It may, or may not, be presented in a rhetorically sneaky way that is designed to obscure the fallacy, but, even if it is, the fallacy is a logical one, and the sneaky use of rhetoric is an accessory to the crime but it is not the fallacy itself.
[edit; it occurs to me that my post invites “frankly my dear"-style mockery, so here is my perhaps futile attempt to steal the thunder of such jabs.]