And even at that, the race started at 1980, but the first time a man on foot won the race was in 2004.
One "man on foot" win in 24 races and that man being a marathon runner, does not bode well with the idea that man in general can outrun horses for long distances.
Look at those times: the best time ever is 1 hour, 57 minutes (horse) for a 22 mile race. That is trivial to beat on a bike.
It is rare for humans to actually be physically capable of it these days, but chasing animals until they collapse from exhaustion is something hairless sweating bipedal are built for. The very best horses could still do it, but attempting persistence hunting on horseback with most horses would probably injure the horse.
Of course horses have been selectively bread for endurance for thousands of years so arguably their achievements are human achievements, but that's beside the point. ;)