The distance the light has to travel isn't the same on the left hand version and the right hand version. Obviously if light is traveling at a set speed in each version, there will be a delay in bouncing between the mirrors on the right side since there is a greater distance the light has to travel to make the route.
That's the point. The amount of space the light has to travel to bounce between one end of the clock increases if the clock is moving. Why? Because it has to move horizontally and vertically, as opposed to just vertically when it is still.
If it is just moving through horizontal space when it is still to get from one end of the clock to the other, but must move through vertical and horizontal space when it is moving, the the shape of the space between the ends of the light clock through which the light moves is different when it is moving than when it is stationary.
EDIT: The problem with your football field analogy is that unlike the ends of the light clock, which never changes, the distance across the 50 yard line and a lap around the whole field is different. In essence, your using two different light clocks. If the distance between the ends of one light clock is 20 yards and the difference between the ends of the other light clock is 100 yds...of course your going to come up with different times to travel between the two ends.
A better analogy if you want to stick with the football field is that it would take longer to run a lap around the field if you "zig zag" from one side of the track to the other, while at the same time moving around it.