We would like to camp at the state park next Thursday October 17th. Unfortunately, we did not reserve a site in advance. I see there are 23 walk in electric sites. Do the walk in sites usually fill up on a Thursday night this time of year?

There is no way to say for sure if the walk-in area would be full, especially this time of year with the autumn leaf colors. I would certainly look for open reservations: https://www.reserveamerica.com/explore/hocking-hills-state-park/OH/960009/overview

I would just always reserve asap, any site you can. Same thing happened to me and my girlfriend