This issues isn't endemic to websockets. I've done this with iframes as well to portscan machines on my LAN. Additionally, the portscan capabilities are even worse than the article states: you can scan any machine reachable from the visitor's machine. Any 192.* address, anything behind your VPN, so long as the time for actively refusing the connection and failing to route are different. I don't know if you can time connections to known hosts to infer things about Tor circuits.

Simply call Date.now() when adding the iframe and when that iframe's onerror event fires then diff the two. I think you can do this with img tags, frames, and anything backed by a network call that lets you observe load failures.

CORS doesn't save you because you aren't trying to reach into that iframe and run Javascript or access the DOM. A CSP doesn't save you because the site you're visiting is opting to do this and can put whatever they want in their CSP.