I just looked at the debug, and it's showing the error:
The page at '<URL>' was loaded over HTTPS, but attempted to connect to the insecure WebSocket endpoint 'ws://irc-ws.chat.twitch.tv/'. This request has been blocked; this endpoint must be available over WSS.
Seems that it's a less secure version, and I need to use wss instead.
Now I just need to find a wss for Twitch that works. What a pain :(
Aaaaaand if anybody is interested, the correct address is: