It is about an old watch - stary zegarek:
TO jest (kto? co?) stary zegarek (Mianownik - Nominative)
On ma/widzi (kogo? co?) stary zegarek (Biernik - Accusative)
On nie ma (kogo? czego?) starego zegarka (Dopełniacz - Genitive)
nie ma, nie widzi, nie lubi, nie nosi (negations require Genitive case)
"nosić" is in fact one of those rare verbs that do show the difference between Present Simple and Present Continuous. "nosi" can mean "wears" or "carries", but not "is wearing" (nor "is carrying").
"He is not wearing = On nie ma na sobie.
This construction unfortunately hasn't been taught, and 'wearing' used to be accepted in most sentences until around a week ago. But well, we finally decided that it's time to stop accepting answers that are actually wrong.
I keep reading this explanation about present simple and present continuous verbs, but I cannot get my head around it at all. I wish there were a way of opting out of parts of the course that I have no hope of understanding. Continually getting this wrong just makes me want to give up the course completely.
By "other cases are unchanged" I/we mean that cases other than Accusative do not change when negated. But the verb "nosić" here takes the whole noun phrase "stary zegarek" in Accusative, so when it's negated, this whole noun phrase takes Genitive.
"stary" and "zegarka" do not match each other grammatically, as Alik explained.