In English, this sounds like talking about their race times, rather than when they are running.
How will the sentence sound like if I replace "run" with "jog"? May I know?
To a certain extent, the different semantics of "jog" do change the sentence because of course jogging cannot be competitive that way.
However, the bigger problem is a lack of a preposition ("at"). I want to know what time you are running at (more natural) / I want to know at what time you are running ("better")
If I say: -What time will Usain Bolt run in Rio? - I am asking about his race time.
-At what time will Usain Bolt run in Rio? - That is the same as asking when he will run.
Of course, context matters a great deal. If I ask my jogging partner "What time are you running tomorrow?" then that sounds like asking when.