Pronation produces significant racket head speed on the serve.
This dated video is not correct and is misleading. It should be replaced to reflect the current biomechanical analysis of the serve. (I'm a big fan of FYB.)
Internal shoulder (upper arm rotation) produces the greatest contribution to racket head speed on the serve as described by Bruce Elliott & associates for the last 2 decades.
Biomechanics and Tennis
Video showing ISR.
The confusion comes about because both ISR with a straight arm and pronation result in the exact same rotation at the wrist. However, ISR is powerfully driven by large muscles (lat & pec) but pronation is driven by much smaller forearm muscles.