Ok, I just finished watching it. It was pretty interesting. Spoilers below if you plan on watching:
Henry Rojas originated the Gorilla in 1980 when he went to a game on the job as a singing telegram employee. He entertained the fans while there and ended up coming back for more and it turning into a full time gig and the Phoenix Suns Gorilla was born. He was the Gorilla for 8 years until he got tired of being behind the mask.
I wasn't aware of it but as BC mentioned, the Gorilla replacement came out of the ASU gymnastic program. His name is Bob Woolf and as BC also mentioned, many of his ASU gymnast teammates went on to become mascots around the league. Woolf was the Gorilla for 20 years before retiring from the Gorilla as in-game entertainment. However after retiring, Woolf didn't know what to do with himself and became depressed. So, after three years out of the main role, he came back and continues to be the Gorilla today at 50 years of age.
For those that missed it, hopefully it will repeat tonight at 7 PM (PT/AZ) during Sportscenter. It starts at the 37 minute mark of the hour long broadcast.