Basically you wouldn’t
Since join/part is unreliable at best, and doesn’t work at all in “large channels” where more that 1000 people are present.
So using chat isn’t a good way to do this, additionally if the stream sniper is using a different name or doesn’t even login to Twitch.
This idea, doesn’t work at a fundamental level. And you can’t assume someone in game is named the same on Twitch.
And even if you could find them and ban them, you can’t stop them watching the stream.
Additionally you can’t get a member of chat’s IP address anyway (all hosts in TMI are anonomised unlike “regular” IRC)