When Henry is sprinting to the trees in one of the last battles it said "he ducked low like a football player" but they didn't have football back...

As pohnpei397 has tried to point out, formal 'American Football' (I presume you are asking about this, as 'Soccer football' hs been around very long indeed!) began in the 1850s and 1860s, and the Rutgers vs Princeton game (see above) was supposedly the first proper one played in the USA. In addition it hs also been pointed out that Crane wrote his novel rather later and so, by that time American football was around.

However, informally speaking, even if we consider that the Civil War soldiers knew the game, it was probably played in some rough form or the other for quite some time and no doubt, was probably derived from English Rugby football. Rugby is very much like American football to look at you know, 'ducking low' et al.

Hope this helps a bit to put things into simpler perspective! Good luck