When they talk about increased sharpness, they're talking about the blades' edges, not their plan shape. The actual edge of the blade is shaped to be somewhat like a dullish single-bevel knife blade:

That does two things: it means that there is only one edge in play (rather than two, as would be the case with an iris blade that is stamped or otherwise cut with its edges perpendicular to its surface); and that there is virtually no reflective surface in the optical path.

I'm not entirely sure I buy the reflective surfaces part, since that can be overcome with a surface treatment, but the single-diffraction-edge part would be significant, especially at smaller apertures. Now, there's "significance" as a theoretical matter, and there's "significance" in practice, and I'm not equipped to actually test the lens independently of the camera or with differently-shaped iris blades. It may simply be a technical flourish, but Fuji do seem to be going out of their way (between the lack of AA filter, different colour mosaic, etc.) to make a bit of a sharpness and detail statement in the APS-C world, and it just may be the case that the cumulative effect of paying attention to a lot of little details (like the iris blades, the geometry of the exit cone, and so forth) are what they think they have to do to make an appreciable dent in the market.