Taxis are normally waiting outside all WDW resorts. If one is not available a Cast Member will get one right away. I don't know what the fare would be but it couldn't be very high for a short distance.
Their easiest option using WDW transportation is to take a bus to the Disney Studios. From there they can get on the Friendship boat to the Boardwalk. The boats run continuous service between the Studios and the Epcot International Gateway and make three stops along the route at the Epcot resorts. It's a nice relaxing ride.
We normally walk between the Studios and the Boardwalk area. The walk to ESPN would be about 15-20 minutes. The boat would take about the same amount of time unless they just miss one and have to wait.