It’s very simple, just overlay (sum) the waves at different angles with different frequencies and amplitudes. The paper explains the relationship of frequency and height. The formula simply pushes points away from the trough in the horizontal and up and down in a standard sine pattern against this which when not overdone can give you an okish wave shape.
Here’s a very quick knockup thing i did in another app using basic formula deformers and expressions and the described simple approach. It’s massively exaggerating the effect of the horizontal motion which makes it look like jello but was there to give emphasis the difference between this and a standard displacement http://www.per-anders.net/general/waves06.mov (the foam was what was more interesting to me though, the waves was 2 minutes work).
To be honest the waveform is pretty hacky, even if you use a correct relationship between the values the result isn’t that pleasing for any primary waves (very cg without a lot of tweakage) and it takes more effort than you want to bother with to make it handle shoreline and other colliders in a believable fashion. But it’s good for filling in a lot of generic watery areas.