Make sure you rebuild with brunch after you run:
$ npm install --save react react-dom
$ brunch build
And it’s not going to hurt to restart your Phoenix server after doing so either. Unfortunately I don’t use Windows for any of my development environments so I may not be able to help if it’s a node/Windows issue beyond that, but I ran into the error you described (except with react-dom) and it was because I had not rebuilt with brunch. Also verify that react and react-dom are in your npm whitelist in brunch-config, since that will also affect the ability to load from it.