Let me rephrase a little and split your question:
Will you be able to mirror your screen in all situations to Chromecast? - No
Can you use it with 3rd party apps? - Yes
I use Tubecast (which is a great app in conjunction with Video 360, same dev) and that will let you cast any video from within the app to Chromecast. I think there are more apps in the Store that provide similar capability.
Windows 10 provides Miracast support, which will let you achieve the same functionality that Android (also Miracast compatible) provides in conjunction with Chromecast to mirror your screen. (Miracast adapters that work very well are, Roku (anything from Stick to Roku 4), Microsoft Wireless Display adapter and many more).
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