Why is American football called "football" even though the players play with their hands more than their feet? It seems to be very similar to rugby, and doesn't have the name "American Rugby". What might be the reason for it to be called "Football" even though it is more similar to Rugby?
American football is called football because of its origin. Its like soccer, can be traced back to rugby football where you use your feet to kick a ball at a goal or successfully carry a ball over a goal line. Over time, some rules were changed such as the concept of line of scrimmage and of four downs and a certain distance required to get more downs and, of course, the forward pass. In earlier times, football had virtually no rules. If you wish, you can trace its ancestry back to the 1600's.
I hope the following link will give pretty descriptive answer for your question.
Gridiron is American slang for the now obsolete field markings every five yards in both directions. This "gridiron" pattern made refereeing simpler when different rules existed for passing, kicking, and first downs. Gridiron was a simple one word designation to differentiate American football from the other two versions of the game back in the late 19th century; association football (soccer) and rugby football.
Before forward passing was introduced (1906), 19th century Gridiron or American football rules allowed a punting team to recover its own punt, hence it was an often used tactic to gain ground, as it is today in rugby. Also drop kick goals were more prevalent and scored relatively more compared to "touchdowns" . Field goals/drop kicks were 5 pts same as touchdowns until 1904. They were also easier because the ball was shaped with rounded ends similar to current rugby ball. Both of these situations generated much more use of the foot/kicking.