Most interests are pretty simple keywords so it'd certainly be possible to do algorithmic matching on the backend. But the article doesn't actually say they'll use profiles to choose drivers. More likely they'll continue sending you the closest available driver (at least at first), and if their profile indicates a shared interest, great, now you have something to talk about.

They see them after they have already been assigned a driver, just like it is now, except now you only see their name and photo. Have you ever used Lyft or Uber?

The point is that if there are things the driver and passenger have to talk about, they will more easily come to light if there is a driver profile available.