You need to upgrade to Blender 2.80 to get this to export. Blender uses .HDR files for environment texture, and they work just fine in BJS. Of course, your World surface must Use Nodes, but that is not a real restriction, since an environment in Blender is only in Nodes.
There are also some custom properties in the exporter to also have the environment texture also serve as your skybox, if you wish.
First, with this exporter, check the log file also written. My guess is you wrote std materials, not pbr. This exporter does both. Std is default. Check box shown in screen shot from previous post of mine.
@JCPalmer I try blender 2.8 beta with the exporter version 6.0 and I have a problem that the meshes change their coordinates at random places.
but with blender 2.79 and version 5.6 of the exporter there is not this problem
What does that have to do with env texture? I have not seen this. Are you trying to use a 2.79 blend file in 2.80, or file appending in meshes, etc? Post your log file.