I've been working on a similar-ish project with native Chromecast support and Amazon TV and using phones/tablets/laptops as controllers. You can give it a look at https://gametje.com (no login required, just continue as guest). It's less jeopardy/trivia and more like Jackbox. Currently has 3 games with the 4th almost done (available for Alpha testers). Was planning on sharing it on HN soon. Playable in 9 languages.
For Chromecast, you can cast directly from your phone and it copies the game code to join easily.
For Chromecast, you can cast directly from your phone and it copies the game code to join easily.