Video.js, and the playback technologies such as videojs-contrib-hls all work in a Webpack based build environment. Here are several configuration changes specific to Webpack that will get you up and running.
In addition to this, you may run into a problem where Webpack does not know how to load .eot files required for IE8 support by default. This can be solved by installing the file-loader and url-loader packages. Install them by running:
Source maps that use the 'eval' tag are not compatible with webworkify, so this may need to be changed also. Source maps such as 'cheap-eval-module-source-map' should be changed to 'cheap-source-map' or anything else that fits your build without using 'eval' source maps.