Jeff Blackburn had a prolific 24-year run at Amazon , helping create and build Prime Video , Amazon Studios, Amazon Music and leading the company’s push into advertising. Prior to the “everything store,” though, he was a former high school tennis standout who came to recognize that a passion for the sport and the long hours required by a famously hard-driving tech culture were incompatible. The exec’s personal and professional backgrounds officially fused last year when he was named CEO of the Tennis Channel by Sinclair, which paid $350 million to acquire it in 2016. After dropping tennis in order to play linebacker on Dartmouth’s football team, Blackburn “gave up the racket,” as he puts it, for 25 years. “I missed it so much, but was working so hard,” he recalls. After rediscovering the sport while still at Amazon, he now plays competitive team matches. “I go out there and battle on the weekends,” he says with a grin. Blackburn’s arrival has coincided with an upswing in ratings and streaming signups.…