God does not care about sports in themselves. God cares about the people who play them.
God cares about the people who watch and enjoy sports and whose lives are affected by sports. And God works through sports, as God works through all things, for the good of those who love him and are called according to his purpose.
Training the body is, or can be, a profound and necessary school for the spirit. And in today’s age, when so many Christians live lives of comfortable complacency, when the rigor and striving of faith have been so terribly deemphasized, sports can serve an important role in reminding us of the importance of discipline and collective sacrifice in the pursuit of a greater goal.
So if sports can help us grow closer to God and more mature in our faith — and they can — then yes, God cares about sports for what can be accomplished through them.