Yes, there's a plugin that lets you do that. I haven't used it myself, but I think it's called Pulser or something like that.

Cool project! I'm sure this was more fun than just getting a Chromecast dongle or messing with nightmarishly expensive wireless HDMI equipment.

Though, to respond to the last point on the page:

Media PC software already exists. However, both Plex and Kodi, to my knowledge, sort of expects you to have a media collection stored on hard drives somewhere.

I cannot speak for Plex, but regarding Kodi, that isn't entirely true. Yes, you can have an existing media collection and use it with Kodi. However, you're not required to, and you can just as easily stream content from the web. I've got a copy of OSMC running on a Pi and I can stream movies and videos that I've never seen before; pretty much anything that I'd be watching at my computer.

For complete disclosure: while I maintain the Pi at home, I don't use it on a daily basis - the only people watching TV in my household are my parents and my brother. But from what I've seen while setting it up and giving it a test drive, it's pretty nifty. It's been in use at home for months without problems.