The Red Sox have been simply "the Sox" in Boston and New England, to the fans, announcers and headline writers in the regional media for decades and probably longer. I believe in Babe Ruth's autobiography he talks about playing for "the Sox." I'm guessing the Blue Jays are simply the Jays in Toronto and among Canadian fans. The Devil Rays were probably the Rays to their fans long before they dropped the Devil. In Pittsburg, the Pirates are the "Bucs" because shortening buccaneer sounds better than shortening pirate. In San Diego, fans talk about "the Pads" as silly as that might sound. At Northern Arizona University, the sports teams, the Lumberjacks are often called "the Jacks." The Yuma High School Criminals are the Crims and Arizona Western College Matadors are the Mats. I doubt that the Scottsdale Community College Artichokes are known as the 'Chokes," but I digress.
The national media referring to the Red Sox as "the Sox," though does sound a bit too familiar, as if the national media were calling the Tigers "the Tiges." The White Sox have "Sox" on their jerseys and caps, but with the Red Sox, the abbreviation is your own.