Correct.
West Virginia and Ohio have a tax reciprocity agreement which prevents double taxation.
Even though your employer is in West Virginia, the taxes have been properly withheld and paid to Ohio. This means you are not a "nonresident."
You will not need to file a West Virginia state income tax return.
For more information, follow this link:
https://www.tax.ohio.gov/faq/tabid/6315/Default.aspx?QuestionID=5436&AFMID=11354
