was the termination of a cavs fan legal over a private tweet

Absent a contract limiting an employer's right to fire an employee, the employee can be fired for any reason not prohibited by statute (e.g. race, religion, gender, etc.)  The first amendment only applies to government action, not the action of a private employer.  Some jurisdicitons have statutes limiting an employer's right to fire someone over political speech, but I doubt very much that Ohio has a statute prohibiting firing someone for tarnishing its reputation by directing obscenities towards a child.