There are three possible candidates, but you may need to "google" since I'm not sure which ones would have existed at that time.
There are the Boitsfort, Sterrebeek and Groenendael racetracks ("hippodrome" in French). Sterrebeek would be the closest to Tervuren, but I have a feeling that it was only opened between the two world wars.
All 3 are on the same side of Brussels as Tervuren, though clearly what today is a 15 minute drive in a car today would have have represented a considerably longer journey in the 1890s.