So here's the setup:
I have a phone running Android 7.1.1. It comes with Google Assistant.
I have a TV, which is connected to a Windows 10 PC. I use it to watch Netflix via netflix.com in Chrome.
How can I use my phone to watch shows on my TV via voice commands? Like "Play Stranger Things on my TV" or "Play Stranger Things on Netflix on my TV".
I know Google Home and the Pixel phones can control Chromecast. Surely there's an app for Windows 10 that will allow me to control it too?
TL;DR: I don't believe there is an official Windows 10 app which will act as a Chromecast client (and I doubt there will be). Buy a Chromecast HDMI stick for your TV.
So I have a 2nd Generation Chromecast connected to my TV and through the Google Assistant on my Android phone (6.0.2) I was able to launch YouTube as well as Spotify.
Netflix is a first party partner for Google Home:
https://support.google.com/googlehome/answer/7214982?hl=en
so voice commands work there. You would still need to link up your account but if you had a Chromecast it should work.
https://help.netflix.com/en/node/23924
While you can cast from the Chrome browser it is either a sender or remote control and not a receiver. My Chromecast does appear to be updated relatively frequently which means that Google can force updates while as a client app (on any OS) it could be blocked. Additionally they would need to integrate their DRM stack into Windows which is even more work.
But what if I wanted to control my PC via Google Assistant
Setup your own server to connect to Google Assistant. You'll have a write a Windows client as well which perform the actions. One blocking point is that you'll need to have it up 24/7 to keep it responsive. If you use a hosting service which shuts it down until request the startup delay may tell Google that the service is no longer working. As always coding problems are off-topic here.
