What is the standard way to use z-score with EEG?
Need a bit of clarity in question. There can be numerous normalization techniques for EEG depending on how they are used. That can be before processing (i.e. raw) or even after processing (for example, with FFT or other transforms).

Z-transform is ONE method. Period. There is nothing else called z-transform. You can have a look on Wikipedia entry of z-transform here.

Z-score, as used in your article, is a statistical measure, also called the standard score. More info here, again.

To sum up, z-transform and z-score are NOT linked.