Does every player have to be in front of the TV to play effectively?

I tried it with some other gamers on Twitch and some game with a fair amount of time to answer (Drawful) are still playable even with the delay. You still have to keep an eye on your mobile device and not count on the actual stream or you'll lose some precious seconds to answer.

It's very possible! Just stream it for them using a service with low latency. I've played Jackbox myself on Mixer (a competing game streaming service to Twitch, owned by Microsoft and integrated into both the Xbox and Windows 10) on multiple occasions and the site's claimed 0.2s delay has held up in my experience.

People across the world are successfully answering questions by buzzing in faster than I am, having seen the main screen at essentially the same time, and I don't have to adjust at all by adding in waiting periods. Generally, during peak times of day someone is streaming one of the Jackbox versions on Mixer and you can join in yourself to test it out.

The entire game screen is shared to those watching the stream, and they don't require any extra info, since they see the same thing you do (depending on the streaming software settings you have in place). The answer options via their smartphone is all they need for drawing, picking multiple choice, typing an answer etc.