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@peertube is the Fediverse's video sharing network. You can follow and interact with PeerTube accounts from Mastodon.
For example, you can follow @theatticdwellers and when they publish a new video it will appear in your Mastodon feed. If you like one of their posts, that will show as a thumbs up on PeerTube, and if you reply to a post it will show as a comment under the video on PeerTube.
More info about all of this (and also how to publish your own videos) at:
fedi.tipsPeerTube: Video on the Fediverse | Fedi.Tips – An Unofficial Guide to Mastodon and the Fediverse
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Fedi.Tips
@feditips @peertube @theatticdwellers Fediverse should have an app for Wi-Fi televisions. I’d watch. Don’t watch videos on my phone. Battery issues. 
PeerTube uses open standards, as far as I know there's nothing to stop a third party app developer doing this.