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