I'd never noticed this term used before but I googled "work stoppage" and "baseball" just now and it's all over the place. ESPN even has a page called Work Stoppage 101. It hasn't completely displaced "strike" but I wonder how it came to be used at all.
The baseball players union is one of the best unions in the history of the U.S. It was built in the '60s and '70s largely by a career labor guy from the Bronx, Marvin Miller, who was trained as an economist. It's a great organizing story. In the beginning the players were so clueless they wanted to appoint Richard Nixon as Miller's general counsel.