Definetely, Waymo is ahead of everybody, but the race is closer than one would think. In addition to Google and Uber, there exist about a dozen smaller players but with competitive technology.

For example, nuTonomy, the start-up at which I work, has deployed a similar trial in Singapore in August 2016. (btw, we are hiring in everything!).

It's not a "race", it's more like a "marathon": there is a big difference in making something that works 99% of the times (sufficient for a trial like the above), and something that works 99.9999...% of the times (a product that can be actually deployed).