Does the HomePod offer 3rd-party apps?
Actually the answer to your specific question is no. Apple will support some (limited) domains (Messaging, Lists, and Notes). Music streaming is not one of them.

SiriKit on HomePod
With the intelligence of Siri, users control HomePod through natural voice interaction and can conveniently access iOS apps that support SiriKit Messaging, Lists, and Notes. Siri recognizes SiriKit requests made on HomePod and sends those requests to the user’s iOS device for processing. To prepare your app, make sure that your SiriKit integration is up to date and that you’ve adopted all of the appropriate intents.
Test the voice-only experience by using Siri through headphones connected to your iOS device with iOS 11.2 or later.

https://developer.apple.com/sirikit/