I don't think sports are dying. Regular football (or soccer) is a massive industry and growing, and basketball is still pretty big. Maybe it's because american football is not that popular outside of the USA, and therefore when something keeps american people more entertained, the sport suffers more? That can't really happen to sports that are popular everywhere like regular football.
Also, it is still too soon for e-Sports to seriously endanger traditional sports. Give them ten years, and we'll see more and more e-Sports rising.










