There are a couple of possibilities here for what is going on.
First, Crane wrote his book in 1895. The Rutgers vs. Princeton game that is usually seen as the first college football game happened in 1869. It would likely have been hard to look up the exact date for the game back in those days and Crane might have just missed by a few years.
Second, the 1869 game was not the first time anything called football had been played -- it was just the first with these particular rules that gave rise to what we now call football in the US. So Crane might have been referring to one of these other types of football.
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
I think that then, football was in it's early stages, or Crane could have meant rugby, which was certainly around at that time. It could have been a lot of sports.
maby he(crane) is just showing a similie to the book reader