Is it an Ohio law if the insurance company can't match the shingles do they have to replace the whole roof?

No, There is no such law.

What the company will pay for the repair of your roof is dependent on what type of policy you bought and the age of your roofing material.

If you bought an HO1, the cheapest Home Insurance Policy then you probably have cash value coverage. The company will only pay to repair the damaged portion of your roof. Match and asthetic issues are generally excluded from coverage under the HO1

If you bought an HO2 or HO3 policy then you may have full replacement value coverage, in which case they will pay whatever it cost to replace the entire roof.

Match issues are addressed in your Insurance Policy Contract you agreed to when you purchased your insurance.