Wait, I thought the check here is first done with random strings, and only if those return NXDOMAIN as expected, then the real search entries that might be hostnames are sent to your configured DNS server (and only after pressing enter).
You're correct, that's what this post is about: random strings forwarded to the DNS roots to establish, without leaking any intent to the user's ISP DNS server, whether DNS NXDOMAINs are being intercepted. There's no privacy implication to this beyond the privacy benefit users get from things that push back on interception.