Maybe what’s going on here is that the specific anime series that I’m watching is Dragon Raja - The Blazing Dawn
And it appears to be based on a Chinese novel - so perhaps the episode numbering such as 第一集 is from the Chinese rather than from Japanese.
I’m watching it on Crunchyroll, with Japanese voice actors and English subtitles - and it’s clear that the names of the protagonist and other characters in the show are Chinese.
So maybe I’ve just answered my own question.
(BTW, I’ve been binge watching 16 episodes, and it’s been pretty good, especially if you’re into dragons and magic and epic battles (which I’m not particularly fond of), or if you enjoy anime shows where the MC is ‘over-powered’ but not especially aware of it, and not especially smart, either.)
To a certain extent, creators can number chapters with whichever format they like, though admittedly the ones I’ve checked all do it by having a different word in front of the number rather than playing with the counter word. For example, Horimiya calls its chapters Page.01, Page.02 et cetera; Komi-san uses コミュ, and Twin Spica uses MISSION: