If you are the broadcaster, +1 to local record.
If you are not the broadcaster, you are either
- Recording it without permission of the broadcaster, so thats content theft essentially,
- Recording with permission,
If it’s with permission you are likely an editor of their channel, so you can download the VOD from Twitch instead, using the tools that Twitch provides. Once the stream is complete. No real need to record it in real time.