In the coarsest sense, to say that Nietzsche's style is important is to say that his writing is unusual and idiosyncratic. This in turn is just to say that his works do not exhibit the features we have been accustomed to expect of philosophical treatises. And, forgetting that philosophical treatises themselves have been written in the most various styles imaginable, this has often been taken to show that Nietzsche's works are not, in some sense, philosophical.
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Alexander Nehamas, Nietzsche: Life as Literature, Ch. 1, The Most Multifarious Art of Style