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I agree with you a photography is art. In art everything is possible, so a faceless portrait isn't that special. But if we look at this photo from a everyday perspective, does a portrait need a face?

Well, the way I see it, a face is what we used to remember things by and identify them later. If a picture is used to convey a meaning or a story which words cannot express, is it really necessary to give it a face?
Of course, the woman might need one. However, the woman is not the picture, but merely a part of it, don't you think?

That is true. If we want to call this picture a portrait, it should probably have a face. But if we call it a faceless portrait that it's ok :) Because it's an artistic expression.

True. Art is, in the end, open to the interpretation of the artist and the observer. That is what separates it from what is concrete. Perhaps the answer to your question lies in the eyes of the beholder. Just like the beauty of the girl in the picture.