In spite of all this American growth in the game, it was slowly losing ground to a newcomer. In many cities, local cricket clubs were contributing to their own demise by encouraging crossover to the developing game of baseball. After the United States Civil War the Cincinnati Red Stockings brought a talented young bowler from the St. George's Cricket Club in New York to serve as a player and manager of the team. Harry Wright applied the "scientific" batting and specialized placement of fielders that he had learned in cricket to his new sport. This development was instrumental in creating the Cincinnati team's undefeated 1869 season. It also helped to secure the place of baseball as one of the most popular sports in the country.
It may have been during the Civil War that baseball secured its place as America's game. An army making a brief stop at a location could easily organise a game of baseball on almost any clear patch of ground, whilst cricket required a carefully prepared pitch. Baseball began to poach players and administrators from the world of cricket. Nick Young, who served for 25 years as the president of the National League, was originally a successful cricketer. It was not until the Civil War that he took up baseball because "it looked like cricket for which his soul thirsted." It has been suggested that the fast-paced quick play of baseball was more appealing to Americans than the technical slower game of cricket. This natural tendency toward baseball was compounded by terrible American defeats at the hands of a traveling English side in 1859, which may have caused Americans to think that they would never be successful at this English game. By the end of the Civil War, most cricket fans had given up their hopes of broad-based support for the game. Baseball filled the role of the "people's game" and cricket became an amateur game for gentlemen.
So, here we have a few major reasons for the crossover:
Many famous cricket players were switching over to baseball. This could be attributed to the next point.
Baseball was quicker paced than cricket. Because, there was no clock, there was no defensive batting, making it more exciting.
Baseball didn't need a special field. This made it much easier for soldiers to play on the move. Obviously, afterwards, they would bring it home and popularize it.
The US suffered demoralizing defeats from European teams.
This page also states that
Baseball suited war-time needs. It was quick, easy to learn, and required little in the way of equipment or facilities. No pitch was needed - just four sacks thrown on the ground, a simple bat and ball.
My opinion is that the third reason had the most effect. With hundreds of thousands being readily able to play baseball instead of cricket, they exerted a large influence of the sports played at home when they returned.