This is the 9945th most frequent Polish word.
argentyński
"Argentyński" means "Argentinian" or "of Argentina."
The word "argentyńskim" is used here as an adjective describing the noun "piłkarz" (soccer player), indicating their origin as Argentine.
Ten zawodnik jest argentyńskim piłkarzem.
This athlete is an Argentine soccer player.
"Argentyńskie" functions as an adjective modifying "filmy" (movies), denoting that the movies are from Argentina.
Uwielbiam oglądać argentyńskie filmy.
I love watching Argentinian movies.
Here, "Argentyńska" is an adjective describing "kuchnia" (cuisine), specifying the culinary style of Argentina.