How can I use Downcast with my Sonos system?
Currently, the recommended way is to connect your Sonos system to an Airport Express device on your WIFI network. This will allow you to play audio through your Sonos system via Airplay. It's unfortunate that an Airport Express is required but including direct support for Airplay in a non-Apple device such as Sonos would require a direct agreement with Apple.
Instructions for making Sonos available via Airplay: https://sonos.custhelp.com/app/answers/detail/a_id/1241
If I can access Spotify, Pandora, etc through Sonos why can't I access Downcast?
These apps are all web-based services, which is what Sonos' supports when it comes to 3rd party systems. Downcast is not web-based, it is a stand alone app. Your subscriptions, settings, and downloaded content are stored directly on your iOS device or Mac so there is simply no service for your Sonos system to connect.
For direct support to be added in Downcast, Sonos would need to create an open API that 3rd party developers could use, perhaps through an SDK, to control Sonos much like Chromecast is currently supported. We'd be happy to add support for this if Sonos ever creates it.
Sonos Customer Support: https://sonos.custhelp.com/app/ask