When a coach leaves, you update the website. You don't wait for the next season. They have an interim coach.
OSU hasn't bothered for nearly a month. It's in multiple locations, including the drop-down menu for the sport page under "Team Info" and on the athletic department staff directory.
He's no longer the head coach. We aren't talking about a shoestring operation at OSU - they just haven't done it. Does it mean anything for the coaching search? Probably not - I was being somewhat hyperbolic in the first post. But they certainly haven't cared enough to update things which means something.
If you were talking about the actual roster, I'd agree, but not with the head coach.