I don't have a Chromecast, so no idea how well this works, but you could probably install VLC and tell NewPipe to "Use external video player" (in the settings) and then have VLC send it over to your Chromecast.

One big problem with this that I can tell you about right away, is that you only get 720p. NewPipe deals with some DRM bullshit to allow playing of higher resolutions, which VLC does not do.