Words in and of themselves are not offensive, its a matter of context.

If someone calls you a stupid f*ing chink, then not only is it offensive, its pretty base; that somehow your race is a bad thing to be called. That somehow by calling someone chinese using that word its an insult.

Good on you for not taking it as an insult. Because logically, its not an insult, its just intended that way by a person who can't even manage two syllables.