This is "stát (o někoho)", not "starat se (o někoho)". Two different verbs with somewhat different meaning. Stát o někoho is very often used about romantic relations like Ta dívka o mne nestojí! That girl does not care about me! That girl does not want me.
But also: Nestojím o tvé peníze! I do not care about your money! I do not want your money!
It's not quite as simple as that: 'take care of...' and 'care for...' are synonymous in your example as translations of 'starat se o...', even though they aren't synonymous in the original sentence where 'stát o...' represents a different meaning of 'care for...' in the sense of liking/loving something/someone.