the original textures are in the Morrowind.BSA file. They are extracted on the fly during gameplay. The only time a texture is overwritten is either when a replacer puts a file of the exact same name in the appropriate folder - or - when an esp is used to direct the game to another file in another folder. The absence of the dwarven spectre textures in the DM mod would not necessarily cause a problem, unless the .esp has indicated they are in another foloder and they aren't there. In which case, the spectres would have great big yellow exclamation points instead of being invisible.
That said, the issue may be with how dark Darker Morrowind is. Vanilla spectres are faint and if your gamma is set too low or possibly too high (look under game options) they could be very difficult to see. I don't use DM, but I have had similar issues with LCD monitors and lower end graphics cards.
It's not that the textures are missing per se, but if you open up the text in the CS it appears completely blank. The dwarven spectres have a "texture" assigned to them, but it's just a blank file... therefore making them invisible. If I just deleted the texture added by DM would my morrowind use the vanilla texture instead? Or, is there anyway I can assign the vanilla texture to the DM texture in the CS? Note: I am completely inexperienced with the use of the CS, so if the answer is yes please explain how!
Also, I am not sure if DM has overwritten the vanilla texture, but it may have. If this is the case, is there a way to extract the vanilla file from the BSA or something?
edit: I am confident that my monitor isn't just too dark either, or my gamma too high, because I do not have a high quality computer and screen (I can actually barely run texture packs, DM is the only one to work for me so far), and I am able to see all the other ghostly creatures of morrowind quite clearly.