Not strictly true, whilst Rugger was a shortened name for rugby football and soccer was a shortened version of aSSOCiation football and was first used in the 1880's mainly by UK college types who like to stick an ER on the end of anything, hence Johnners, Aggers, Blowers etc.
We generally always used the term football well before the USA started to shorten gridiron football to simply football.
So whilst the term did originate in the UK is was only ever really a nickname, we didn't switch to football because of the American usage of the word soccer.
