I was getting errors in where it is looking for cesiumWorkerBootstrapper in the compatibility folder. If I put it in there where it is looking, it then is looking for one another directory down, and so on. The initial directory it complains about is: client/compatibility/Workers/cesiumWorkerBootstrapper.js. I was able to see that following the suggested approach the textures were loaded, however. I ended up modifying Cesium.js wherever it referenced cesiumWorkerBootstrapper, and moving that entire directory under public, but that didn't work.
Later on I was messing around and trying it with Firefox to see if I could get anymore insight and I got this error: Error: WebGL: A texture is going to be rendered as if it were black, as per the OpenGL ES 2.0.24 spec section 3.8.2, because it is a 2D texture, with a minification filter requiring a mipmap, and is not mipmap complete (as defined in section 3.7.10). I always just end up with the black globe with the glow around it.
My experience with require was on a much smaller scale and took some getting used to, so seeing the main.js file in the require-based release is a little mind boggling.