It gives you a list of directly depended-upon packages. It doesn't give you a list of _those_ packages' dependencies, or _their_ dependencies, which funnily enough also get installed when you install your direct dependencies.
Plus I forgot to address this in my earlier comment: that visualizer only shows dependencies. By default it doesn't load any dev dependencies. You can confirm that for yourself by checking out https://npm.anvaka.com/#/view/2d/rollup for example - only the single runtime dependency on fsevents shows up, the dozens of dev dependencies Rollup has don't.
So yes, React Native does ship that overcomplicated graph of dependencies to all its users. I'll grant that at least _some_ of the code in those dependencies gets tree-shaken out.
Your last paragraph is a bit inaccurate. The dependencies are needed by people developing WITH React Native as opposed to devDependencies (which are for people developing ON React Native). So whilst you will be using the complicated graph of dependencies at some point, that isn't the same as saying they'll be shipped to end users of the app.
The line between dependencies and devDependencies got blurry the second npm packages got used for more than just Node.js itself. What's really needed to remove the ambiguity is something like prodDependencies, which would be a subset of the current dependencies, but I don't know if it's really worth it.