I have been following the platform for a bit now, and it looks like they are in it for the long haul. From an interview with some of the developers working on Stadia, they have also confirmed it.
Of course they can just be saying that but here are a few other things that imply they are sticking around:
It's extremely rare that Google scraps a service with a subscription option.
They have also bought out game studios, and have made 3 of their own game studios (1 in Japan, Canada and England).
They have been working on also integrating this service with YouTube, where you can live stream games and let people watching vote on outcomes in game and also let viewers join your game. These features are still in progress but they have been rolled out for a select set of games.