Says who?
Isn't for the US Supreme Court to make this determination? If they choose to take the case, Ohio cannot stop them.
The Ohio Constitution says people have the right to bear arms for their own defense. The Second Amendment to the US Consitution says that "the right to keep and bear arms shall not be infringed". If these two clauses are in conflict, Ohio loses.
The Supreme Court has no jurisdiction over an issue concerning a state constitution UNLESS a federal question is involved. The court here only ruled that the Ohio Constitution doesn't give the right to concealed carry. Now, the 2nd Amendment might grant the right to concealed carry, but that would be a separate lawsuit. This was just a question of what the Ohio constitution said.