[MarkusQ]

Meta nit pick: You are conflating linguist's jargon with mathematician's jargon.

In much the same way as physicists co-opted common words (e.g. "work" and "energy") to mean very specific things in technical contexts, both linguists and mathematicians gave "ordinal" a specific meaning in their respective domains. These meanings are similar but different, and your nit pick is mistakenly asserting that one of these has priority over the other.

"Ordinal" in linguistics is a word for a class of words. The words being classified may be old, but the use of "ordinal" to denote them is a comparatively modern coinage, roughly contemporary with the mathematicians usage. Both come from non-technical language describing putting things in an "orderly" row (c.f. cognates such as "public order", "court order", etc.) which did not carry the load you are trying to place on them.

[layer8]

There is “zeroth” though as an ordinal humeral, which was already used long before computers came around, as for example in “the zeroth power of a number” (according to Merriam-Webster). So it’s still not quite unambiguous. :)