Interesting that no one else appears to have reported this problem. When I opened the mesh in NifSkope I could see at once that the textures have absolute paths instead of relative ones, meaning that although they are from the vanilla game, they can only be loaded if the game is installed in the exact same folder that is specified in the mesh, namely "c:\bethesda softworks\morrowind\". So, what you need to do is open the file in NifSkope, and for each NiSourceTexture block remove everything up to "textures\..." from the file path, so that for example instead of "c:\bethesda softworks\morrowind\data files\textures\tx_dwe_metal03.dds" it only says "textures\tx_dwe_metal03.dds". You may have to expand each of the NiTriShapes to find the NiSourceTexture blocks if the block list is set to be displayed as a tree, or change it to "Show Blocks in List" in the View menu under "Block List". Once you are done, save the file and it should work.
I hope I could help you, since I don't know if you have any experience with NifSkope at all. If not, come back to me and I see what else I can do.