The title is a little confusing as DNS over HTTPS is the technology that comes to mind for DNS privacy. That hides the DNS queries in an HTTPS tunnel, which means fewer actors can see or spoof DNS results.

The QNAME minimisation technique described in the article is about showing only partial requests to intermediate authorities in the DNS hierarchy. DNS over HTTPS can protect the request until it gets to the resolver, and then the QNAME minimisation system can hide it from interested intermediate DNS authorities. I guess in practice this means the .com servers can't tell whether someone is going to xxx.substack.com or yyy.substack.com just that they're asking about substack.

As the article points out, most users ask a shared DNS resolver to perform resolution for them, and if you want to, the Cloudflare public resolver 1.1.1.1 uses this technique.