I have tested your map locally and have found no problems with cubemaps.
I looked inside your BSP using GCFScape and the only thing I can see which may cause problems is that the filename of the map was changed before cubemaps were built, leaving the VMT files it was given during the compile process in a directory where they won't be found by the game.
Your map name is pl_eclipse_b1, and that's where your cubemaps live inside materials/maps in the BSP. The map used to be named pl_eclipse_b1_88_release and inside that folder in materials/maps in the BSP are the VMTs that the compile process created. I do not know what these VMTs are for, but I think they are to do with cubemaps. Perhaps certain graphics cards or graphics configurations need them? Maybe the game uses them to replace cubemaps with a default cubemap in some situations.
You could try testing a map where the VMT files I mentioned are in the correct folder inside the BSP. This would mean you take one of your '##_release' BSPs and build cubemaps for it, then test it on the laptop. If it works, then you should look at compiling your map using the proper filename, or using a tool like Notepad++ to do a find+replace on them all to change the directory, and then pack them in the correct folder inside the BSP.