That link defines it in terms of simulation as well: "The term "real-time" is also used in simulation to mean that the simulation's clock runs at the same speed

That link defines it in terms of simulation as well: "The term "real-time" is also used in simulation to mean that the simulation's clock runs at the same speed as a real clock." and even states that was the original usage of the term. I think that pretty much meets the definition of "you can watch it happen". Essentially there is real-time systems and real-time simulation. So it seems that they are using the term correctly in the context of simulation.