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I suppose this is more of image sharpening rather than reconstruction. Is this very different from technology on cameras/phones that tries to reduce of photo blurness due to unsteady hands?

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What makes you suppose that? On an abstract level, you can model blur and camera shake with a convolution kernel. You can then invert the kernel and get back the original image. As an analogy, imagine that someone gives you an audio file with an echo. You can subtract the echo with a filter. Camera shake is harder because of the extra dimension. (Of course, you only get back the exact original in the world of mathematics)

Should hopefully get easier with a dedicated asic crunching on the extra dimension gathered from future built-in gyroscopes in cameras.

I don't believe the echo is a simpler example. It's just as complicated as blur really. You can remove both to a large extent, providing you have the correct model with correct parameters. Discovering right parameters is a hard problem in both cases.

What's the difference between "sharpening" and "reconstruction"? Both take an input image, apply some filter which is the best estimate of an inverse of a filter originally applied (e.g., wrong focus).

The technique to unsteady hands artifacts often has access to motion data, which this thing does not.

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