This article's word choice using terms like "larping" and "cosplaying" to talk about Mark Twain on a history site seems like a less than ideal writing style; it made me stop reading and facepalm for a moment.
Did you read the article? It's a stretch to call it an active military unit. As Twain himself wrote, the only maneuver they performed was to retreat, which they barely even knew how to do.
It’s less the formality and more the hypermodern idioms that feel out of place (what’s the opposite of anachronistic?) in talking about a historical subject. Like, yes Mark Twain had the rizz and the Confedussies took the L but that’s probably not how I’d discuss it.
In this case? Anachronistic still. Anachronistic just means something like "belonging to a different time period," and it doesn't strictly imply earlier or later.