Does that mean my theme would be listed in everyone elses plugin list? It's a custom theme for my site, not something I want to publish
Yes, that is correct. Because you've published it to npm, our package manager automatically picks it up as an available theme and offers it for download to any other NodeBB.
You can set nbbpm.index to false in your package.json, but this would also remove the theme from your plugins list.
The easiest thing to do would be to publish the theme under your own namespace (agian, with nbbpm.index set to false), and then install it via the command line, as @pitaj suggested.
e.g. npm i @jimbridger/nodebb-theme-mytheme