The argument is that the presence of horseback riding (and now race car driving) doesn't necessarily diminish the popularity of foot races. Not that horse racing is less popular now (though that my be, simply because it's no longer anyone's preferred method of transportation...)
Ah, I missed that. It's hard to say with certainty whether horseback riding diminished the popularity of foot races since it happened such a long time ago and at a time where probably neither was considered a sport or entertainment.
I do think that technological advances in general affect the appeal of certain games and sports by rendering them less mysterious or by bringing them further from a real world activity/situation.
Of course, I'm talking about relative, not absolute, popularity. Chess and horseback riding will remain popular for a long, long time.