Actually a pretty good job
If you rotate pixels about a central point, the chances of a rotated pixel being moved to the exact location of another pixel are extremely small - unless the rotation is by a multiple of 90 degrees.
Once the pixels are rotated, they then have to be "averaged" - a pixel of the final image may contain contributions from up to 9 rotated pixels. You can see that the effect is more marked nearer the centre of the image - because there are fewer pixels to contain the information at tighter radii.
The left eye has survived so well because it's a circular feature at the centre of rotation. The face also looks quite clear because a large circular ring around the eye is mostly skin tone - distortion is visible but the human mind's ability to directly identify faces and facial features makes it relatively unimportant. The "swirler" would have been better advised to choose a different, asymmetrical point of rotation.
This sort of image manipulation is seriously lossy. As such I am very impressed at the amount of detail that has been recovered. I just tried swirling and unswirling a picture of my son - with much the same results.