You realize SWA is footing the bill to build the terminal 100%? This is as free market as it can get, If the other airlines want to play, let them build their own gates.
You might own this new Hobby terminal, but Mexicans for example, definitely own Mexico. So if these foreign govts take exception to the fact that their own airlines can't get a fair shot at Hobby customers, don't be surprised if they limit your flying.