How is an AES S-Box cyclically shifted to the left?
Yes they are talking about shifting each individual byte.

In the example in the paper, s-box input 00 becomes input A4 (output 63), 01 becomes A5 (7C), and so on. This is a 92 byte left rotation of the s-box elements, which is equivalent to a 164 byte right rotation, all done mod 256.

Without going into extreme detail, I would strongly recommend against using this... ever, it is not a good idea, and actually makes the cipher weaker. There are only 255 new s-boxes generated using this method, and they are all weaker than the original.

The example s-box given shows the following properties:

Differential Uniformity: 8 (lower is better)
Non-linearity: 94 (higher is better)
AutoCorrelation: 88 (lower is better)
SSI: 260608 (lower is better)


The AES standard s-box has these values for the same properties:

Differential Uniformity: 4 (lower is better)
Non-linearity: 112 (higher is better)
AutoCorrelation: 32 (lower is better)
SSI: 133120 (lower is better)


The new s-box also inherits the undesirable properties of the original, such as simple algebraic representation and CCZ equivalence.