Uber started showing up in Google Maps on my phone when I installed the Uber app on my phone. I just assumed there was an interface whereby apps could tell Google Maps "I can get people places".

I don't have any ride-sharing apps installed. Uber just showed up as an option in the directions section below car, walking and public transport, along with an estimated fare cost and 'first ride is free' offer.

I can't find the details now, but I'm sure I once saw an API provided by Maps on Android which allows any app to register itself as capable of providing directions or transit information.

Including those that are not installed on the device?

I've only ever seen Uber listed when I have their app installed.

Or maybe they're the largest ride-sharing platform?

Google Now integrates with Lyft instead of Uber, so it's not necessarily consistent across Google products http://insidesearch.blogspot.com/2015/01/google-app-update-g...

Perhaps it's because Uber is the only service with such an offering?

According to the folks in charge is unrelated.