I originally posted this as a comment because it is an opinion and I couldn't think of any way back it up. As there have been other answers without supporting references I thought I would add this as an answer.
I believe that the reason for the plural names is that those areas of sporting endeavour contain multiple disciplines (athletics, gymnastics) where the different events require different skill sets. In the case of athletics most runners do not jump or throw things, most jumpers do not throw or run (except to gain momentum for their jumps) and most throwers do not jump or run except to gain momentum for their throws. The exceptions are the tri-, pent-, hept- and decathletes.
At the other extreme there are people who compete in named sports where there is a knockout or league competition but they are competing multiple times in a single named sport (badminton, tennis and beach volleyball for example)
In between there is a class of sports with many different competitions which all require excellence in the same skill (examples are swimming, boxing, cycling and fencing)
There are still a few sports where the name does not fit this pattern (for instance horse riding which could qualify for an 'ics' ending by its diversity), archery (which would have to have an 'ing' ending if it were to fit the pattern) and Karate and Tae Kwon Do (which would have an 'ing' ending if the categorisation were strictly enforced) but the names of these sports are historic. As Dan said in a comment above "life is messy".