Hi,
This example was broken when accessing cesiumjs.org over https instead of http. It was fixed in #2827 which will release with Cesium 1.11 at the beginning of July.
As for your own server, it could be a few things. Browsers will complain if you access an http imagery server when the web page itself is accessed over https. It could also be a CORS problem. See the Cross Origin Resource Sharing section of the Imagery Layers Tutorial. Use the console in your browser’s debugger to see if you’re getting any exceptions or error messages. Sandcastle has a console, but it unfortunately can’t include CORS-related error messages.
Kevin
Hope that helps.