The reason it looks likes a park is because it was a park – a roadside park/picnic area maintained by the State of Ohio. The earliest mention of it that I could find online was from July 1949, when an Amherst group held a picnic there.
By 1954, there were three such roadside parks in Lorain County: the one in Vermilion, one on Route 10 about a half mile east of Oberlin, and one in Sheffield Lake on Route 6 at Abbe Road.
But all good things must come to an end, and the State eventually decided to vacate these types of roadside parks that were within city limits. And so the park in Vermilion was closed, as noted in the article below, which appeared in the Journal back on May 29, 1963 – just in time for the summer picnic season.
What's interesting is that the State never owned the land, as explained in the article. It merely leased it from the owner, who continued to pay taxes on it during its time as a public facility.