Yes, he did, and it's not an episode that reflects well on him.

Poor Topsy was considered a rogue elephant, having killed several people (including her abusive trainer), so she was under sentence of death anyway -- but electrocution is hardly the same as being humanely euthanized. And as the book in the game says, it was all a publicity stunt -- Edison's attempt to prove that AC current was deadly dangerous and everyone should install the DC current that was making him rich. Ugly.