This is not a very good circuit, and is not complete. The circuit is three stages of active filters, a gain stage that drives the output, and a final active filter stage that goes nowhere. His gain and phase plots show that significant amplitude and phase distortions will be added to the original signal. I'm not an EEG whiz, but this seems like a lot of thumping on the signal unless you are tryi8ng to extract one specific feature.
Thee is no reason not to use both sections of the dual opamps (or a quad opamp) instead of only one section in each.
MISSING is the stuff in from of the AD620, the circuit that receives the signals from the sensors. Kinda important stuff.
ak