Could be some trouble for Kasich as this ruling will highlight the gay marriage issue for voters. He has to back the gay marriage ban for the base, but that position is a net vote loser.
Will he, though? I can see him doing what Christie and Martinez did and just accept the ruling. Kasich should have no trouble keeping his base together.
Except unlike in NJ or NM the issue isn't resolved by this ruling. It only requires recognizing other states' legal gay marriages as valid, but doesn't legalize gay marriage itself in Ohio. That issue will still (I believe) be on the ballot in November.
Also, the anti-gay marriage base in OH is stronger than in either NM or (especially) NJ.