I think he's basing the date on the assumption that we'll have searched 1 million star systems by 2037 and there are a few million broadcasting societies.
Personally I think the odds are pretty damn long, even on the optimistic end of Sagan's and Drake's assumptions. Assuming there are 200-400 billion star systems in our galaxy, that gives us a 1 in 200-400k odds of finding one by 2037? I'll take the bet.
Still a great read, I'm much more fascinated by the idea of artifacts. I believe that the longer we go without finding things, the more seriously we should be thinking about leaving things.