Meanwhile, the Philadelphia Whites were playing Hartford in Cincinnati on the 21st and winning 13-8. Also, they played Chicago in Cincinnati on September 23, winning 5-0. Philadelphia played three league games in Cincinnati in three days against three different opponents. So I think it's safe to say that the Philadelphia club was the impetus behind the league games in the Cincinnati area.
The question I have is whether or not the game between the Brown Stockings and Philadelphia was scheduled before the two clubs arrived in Cincinnati. I don't think that it's totally clear. There is no advance mention of the game between the two clubs while the paper does mention the upcoming games with the Stars and Luds. Is it possible that the two clubs happened to me in Cincinnati at the same time and decided to get in a championship game while they had the chance? More research is certainly needed and I don't have easy access to the necessary newspapers in Cincinnati and Philadelphia. It would be interesting to see if the papers in those cities mentioned the game in advance.
However, the game doesn't fit the scheduled pattern of the Brown Stockings' league games. It stand out like a sore thumb. It's possible that the club had scheduled some games against local teams in Cincinnati during a lull in the league schedule and Philadelphia, for whatever reason, had scheduled some games in the area as well towards the end of the Brown Stockings visit. Once the two clubs realised that they were both in town, maybe they decided to arrange a match. One possible reason the game was played in Ludlow rather than in Cincinnati (like Philadelphia's games on September 21 and 23) is that it was arranged at the last minute and the Luds' grounds was the only available park.
Tomorrow: The long awaited, heavily anticipated and certain to disappoint post on the Brown Stockings/Philadelphia game in Ludlow, Kentucky.