There are a couple issues in the project that are causing the differences between WebGL and the Editor.
1. The Quality mode for Standalone is set to High Fidelity, but the Quality mode for Web is set to Balanced. The render setup was done for High Fidelity but not Balanced, so the web build will not have any of that render setup. Change the Quality setting for Web to High Fidelity to get the same render settings.
2. ModCubeMaterial points to GeneratedFromGraph-ModCubeShader. It looks like the Cull mode was edited for the shader. But it was only changed for the first SubShader, which excludes the GLES renderers. There is a second SubShader that is for the GLES renderers, and the Cull and Stencil values were not changed there. I copied the Render State values from the first subshader to the second one so that the GLES and non-GLES subshaders are consistent.
After I changed these two things WebGL rendered in the expected way.
The same issues would have been seen if you changed the Standalone graphics API to OpenGLES3.