During their initial season in 1857, the Liberty defeated the Union Club, reportedly the other New Brunswick team playing the New York game. According to a lengthy article in the New York Clipper (October 10, 1857) flushed with victory, the Liberty issued a challenge to any nine New Brunswick men to play them in a "modern" game of base ball. Supposedly the challenge was "undoubtedly intended for a party of Old Fogies'" who played the "old fashioned" game, "which as nearly everyone knows is entirely different from the game as now played." The article which appears to have been written by an "Old Fogie" or someone sympathetic to that group clearly states that the Old Fogies were not a club.
Nine members of the group, now called the "Foundlings" accepted the challenge and asked for the rules of the New York game. Behaving in a very unmanly manner, the Liberty refused so the young men obtained the rules from the Clipper, selected a side and an umpire and practiced four times. However when it came time to play the match, only five of the "Foundlings" were present forcing the addition of four men who apparently didn't know the rules of either game. The article goes on further criticize the Liberty's lack of sportsmanship including stating that John Van Nest of the Liberty who served as umpire was not a "man of some honor."
It's a shame that the article doesn't provide any information about the old fashioned game reportedly played by the Old Fogies, but its one more piece of evidence that when the New York game came to New Jersey it didn't enter a vacuum. There may be a possible clue in the book Athletics at Princeton which devotes significant detail to the introduction of base ball at that nearby college. Reportedly in 1860, the Nassau Base Ball Club of Princeton (effectively the school's team) challenged Rutgers as well as Yale and Columbia to base ball matches. All three schools declined saying they didn't have a base ball team, but were still playing "town ball or the old Connecticut game." It's not clear (at least to me) whether the author meant that the "old Connecticut game" and town ball were the same thing or the three schools played one of those two games, not the New York game. Given the small size of both Rutgers and New Brunswick at the time, it's certainly not impossible that the college students and other young men were playing the same form of "old fashioned" base ball.