Well, Bill Mullins found an 1898 Sanford fire insurance map of Chester that shows the ballpark. It’s pretty definitely the same park, as it’s on 12th Street, and the Chester Times called it “Twelfth Street Park” in 1902. While there’s no indication of where the fences were (and no guarantee that the park hadn’t been altered since 1898), this might give us some hint about its dimensions. Going by the scale at the bottom, and granting some space between the grand stand and home plate, it looks like the right field fence would have been quite close (certainly much less than 300 feet down the line) while left field was substantially farther out, and center field was potentially quite spacious (relatively speaking, anyway).
In the second inning, “Wilson led off with a home run over the right wire…”
In the third inning, “Wilson repeated the trick and lined the ball over the centre field fence after two men were out and the umpire had called two strikes on him.”
In the fifth he struck out.
And in the eighth he homered again to help seal the game, but no details are given.
I don’t have any idea whether Wilson hit left or right-handed (or was a switch-hitter), and again we don’t know where the fences were exactly, especially in center field. But right field was probably quite close, and the mention of “the wire” indicates that there might have been a high fence or barrier there to compensate for the short distance.