I recently developed a plugin to enable live video broadcasting. I may have published on NPM a bit prematurely - have not tested yet. I would appreciate help testing and debugging the plugin, hosted in this git.
After some more code digging and experiments I can answer my own question. A theme is a normal plugin and as such does not inherit any behavior from other plugins.
So you need to copy everything you need from the base theme library.js to your child theme. And of course, you need to declare client scripts explicitly.
Loading of missing templates from base theme is the only link between the base and the child theme.