When you mentioned amusement park in Ohio I thought you might have been referring to Time Out on the Court in Forest Park, OH. It was kind of a mini amusement center that had kiddie rides, bumper cars, and a Ferris wheel all situated inside a mall (which is now mostly dead except for Kohl's as the last anchor and a lone retro game store/arcade in the center).
Anyway, back in it's heyday, besides the stuff mentioned above there was also an arcade, a laser tag arena, and an area devoted to VR machines. They were the Virtuality machines that ran the game Dactyl Nightmare and there were also sit down VR units as well.
https://www.youtube.com/watch?v=L60wgPuuDpEI couldn't find any videos for the sit-down version but this is the game that was running in the stand up units. It was by far the more popular of the two that was offered though it used to get super annoying when people would get in and not listen to the instructions. Had plenty of drunks try to play (there was a Buffalo Wild Wings across the hall) and it was fun to mess with them. I would strap these yahoos in and when they would not listen to me, I would hit a button on the keyboard that perpetually had the pterodactyl go after them.
The other reason I thought it might have been this location was because at one point we had a LAN set up for 8 computers called Wired4Play. Like I said, it was 8 computers networked together to play games like Doom II, Duke Nukem 3D, and Rise of the Triad. A lot of us who worked that booth were computer nerds so we were adding custom .WADs to the Doom II game where the Imps would sound like Beavis and Butthead among other things.