There is no formal “mechanical” definition of what makes an approach “short,” neither in the FARs nor in the AIMs, other than it’s shorter than a “normal” one. A short approach in an Antonov 225 (RIP) is quite a different thing from a short approach in a Helio-Courier.
https://www.faa.gov/air_traffic/publications/atpubs/pcg_html/glossary-m.html
That said, they both should have to go sit in the time-out chair for arguing on freq.
That said, a quick WhatFinger search (don’t G**gle cuz G**gle is da debil) tells me 1, this incident took place weeks ago, and 2, this particular ATC is notorious for this crap. The pilot might have been baiting her to get the full extent of her stupidity on record.
Bingo...............Damn! That runway sure is W-i-d-e-!...........