That doesn't mean that all the horses run at the same speed - it just means that an individual horse doesn't speed up or slow down while running - if its average speed is 17.2 MPH, it runs at 17.2 MPH for the whole course.
Yeah, I thought of that - but do people look at average speed when timing a race? I was reading the whole sentence in "... you don't have a stopwatch and all horses run at a constant pace." :-)