Thanks for your question. Unfortunately, anything you specify in Sandcastle (which is what you access when you click Open complete code example) is a front-end change that does not affect the data itself, which is why you aren’t seeing it in Cesium Stories.
Cesium Stories attenuates point size based on screen space error, in order to ensure the right size is used depending on the density of the points that are displayed. You can style your points by pressing this button beside your asset in the Assets panel of your Story:
(More documentation here, although it will be a little different for points vs. meshes.)
However, as you may have already observed, this does not allow you to change point size. If you tell me more about the problem and about what you are trying to achieve, I can open a feature request about this. Do the points not look right to you? Are they not at an optimal size when displayed in Stories? If you have a Cesium Story you can share (or just an ion asset ID), that would be helpful.