In short, professional sports is part of the mix of amenities that makes people want to live and work in a place. Mariners and Seahawks games are broadcast over the entire state. Groups from Spokane, Walla Walla, the Tri-Cities, Othello and Asotin come to the games in Seattle as do people in Cathlamet and Aberdeen. In other words, these are Washington state teams, not Seattle teams. Businesses outside Seattle need to support professional sports because those teams will help lure new workers and keep the ones already here.
Pro sports makes a community a complete place to live and work.
The Mariners have been losing money since the beginning, and much of the reason is because the owners of the major league teams refuse to share television revenues. But a good part of the reason is that people don't like watching baseball indoors. It is unnatural. Baseball is an outside activity whether you are playing it or watching it. The case for the Seahawks is a bit muddier.