Wow! If that were the case than couldn't this person also sue people who use the word 'cosplay' on their sites? Or sue people who say that they 'cosplay'? Or for holding private 'cosplay' photoshoots? This person could get very rich fast...Riiiight

...If that's the case everyone has to start spelling it as kosupure to avoid trouble. *lol*
But yes, a trademark is like the coporate identity of a company so to avoid that same logo/word from being used by another company and causing confusion amongst consumers or what have you, they trademark it. Usually they're logos and words of a certain font, color and type face. This is to establish their identity as a corporation/company. i.e you can't use that word in that color or font since technically it is their so called 'logo'.
But somehow I find the details of that particular trademark rather vague...any law students lurking around here?