The 5800X would be more than suitable for your needs, unless you have other multitasking needs that require far more computing power.
Watching shows and streams is basically nothing for high-end equipment; if playing your game is like driving a car, checking out a Twitch stream is the equivalent of scratching your nose, a task that would tax nobody driving a car.
Now, if you do any streaming yourself that's a different story. A 5900X certainly won't hurt you, but unless you have tasks that really utilize those cores, you're just spending money you don't need to. By the time you actually would need 24 threads for a game instead of 16, both CPUs are likely to be poor performers.