I contacted email@example.com and received this response:
Thank you for contacting the Cox Social Media Support team. We do not have any specific information on what will be used to replace flash at this time, but we will have an alternative when that time comes.
Cox Social Media Support Specialist
Thank you, Maria. It's somewhat reassuring to hear from someone at Cox that there are plans to update watchtv.cox so that it will continue to be available after Adobe retires Flash Player.