Apparently the pimienta negra chica or pimienta chica is what is known in English as peppercorn. There is a different spice, pimienta gorda, which is known in English as allspice.
My first source was an article at https://www.imco.mx/productos/pimienta-gorda/. It was corroborated at https://www.laprensagrafica.com/mujer/Los-tipos-de-pimienta-20140317-0154.html. Next I did a google images search for
pimienta negra chica y pimienta gorda comparison (I know, I suddenly switched languages in the middle of the search phrase -- but hey, it worked). I found the following helpful image, which used to be posted at https://ok-salud.com/ but which is no longer there. Warning for the squeamish: please be aware that there are images of endoparasites on the home page of ok-salud.com. At any rate, the comparison picture of the two spices is quite helpful:
In the video you watched (thanks for the link!) she clearly adds three separate spices ("pimienta chica, pimienta negra y un poquito de clavos"). So it seems this cook's name for these two spices doesn't match up exactly with what I found. At any rate, her recipe seems to include black pepper, allspice and cloves.
Food names vary from one region to another more than anything else I know. It could be a regional thing or it could be that she misspoke, or that she has her own pet names for these spices. I did check some online recipes, and what I commonly found was "pimienta negra" and "pimienta gorda" (listed as separate ingredients).
(I wish someone would get Doña Ángela a deeper wooden spoon so she has an easier time fishing the round tomato halves out of the hot oil....)