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A texture with that purple-and-black checkerboard uses
specularity - you know, reflections and stuff. In order to make them work properly, you need to build cubemaps, which basically create the reflections for your map.
Basically, place the env_cubemap entities in places like this where reflections are used. When you compile your map, enter "buildcubemaps" into your console while playing it. If no change is noticed, try restarting the map. Good luck!
You may also want to read
this article on the Valve Dev. wiki for a deeper understanding of how they work.