No, it doesn't. The surgeons I work with don't do prostate manipulation when they insert the scopes, but my guess is that it's a way to straighten out the urethra to assist with scope insertion in awake or lightly sedated patients (with local anaesthesia).

Update: I ran into an actual urologist in the change room and showed him the diagram. He said the only time he would apply pressure like that is to improve the position of the prostate during a prostate resection, but not just to do a cystoscopy. I asked if this was more common during direct vision cystoscopy (using your eye to see down the scope rather than a camera unit as we do now), and he said he didn't think so but wasn't sure. This guy is not that far off retirement, so he's been around long enough to remember a lot of advances in technique and technology. I think this diagram belongs in a museum.

Phobophile rules.