1. We say a point man (usually a defenseman) at the offensive blueline on the powerplay is quarterbacking the play (not all point men on the PP do this, but many do, as the go-to guy like a point guard at the top of the circle in basketball, deciding whom to dish off to or whether to take a shot himself.
2. A center like Bobby Clarke and Wayne Gretzky had an "office" behind the net on the powerplay, bringing the puck there and the defending defensemen have to decide whether to cover the pass (like man-to-man coverage in football) or else to rush the puck carrier from one side of the net, risking leaving that player open to wrap around the other side for a quality scoring chance himself up close to the crease.
3. On a regular shift, a guy like Joe Thornton or Ryan Getzlaf (and Oates, Gretzky, Federko before them) would bring the puck into the offensive zone (carrying it across the blueline first and avoid an offside pass) and then pivot or change direction and stay high, causing the defenseman covering them to come to an abrupt halt and decide whether to try and check the puck carrier or get ready to intercept the pass or cover the man coming late who is looking to receive the pass. THAT is also quarterbacking a play, but at even strength.
4. A guy like Petr Forsberg looked like a scrambling quarterback from football in that he held onto the puck, weaving around, looking to pass to an open guy, taking heat from opposing players trying to strip the puck from him or knock him down.
5. Wingers could also quarterback, in the traditional hockey sense when they are the point man on the powerplay or on a regular shift if they act like Forsberg (Jagr protected the puck and prided himself as a passer) or simply used their speed and maneuverability to avoid contact while looking for the right pass in the offensive zone (Martin St. Louis, Alex Tanguay). Is Patrick Kane a regular shift quarterback in the offensive zone in this sense? Sometimes, yeah.