namayake, when you are opening the Civ 3 Complete folder, you will see a structure like this:
It shows the files for Civ 3 Vanilla and the folders for the expansions Civ 3PTW and Conquests. Please don´t zip the CCM2.50 files into the Civ 3 Vanilla folders. Such an action could cause the problems, that you have shown in your two screenshots.
1. Now select the folder Conquests, that holds the files of the expansion C3C (marked in the screenshot above with a red arrow).
2. The folder containing the C3C files will open and you will see a structure like that, but the folders Art-orig, sounds-orig and Text-orig (all marked with blue arrows are not existing yet. You are now in the folder that holds the C3C mainfiles, especially the folders Art, sounds and Text (all marked with red arrows in the second screenshot).
3. Now please make copies of the folders Art, sounds and Text (all marked with red arrows) and name these copies to Art-orig, sounds-orig and Text-orig (or give them another suffix you like. These copies are the folders marked with blue arrows in the screenshot above. The copies, marked with the blue arrows, serve to return quickly to the files of the original C3C expansion or to restore the C3C expansion, when something went wrong with your installation of CCM2.50 without needing to do another download and installation of Civ 3 Complete at GOG.
Also make a copy of the conquests main biq and name it conquests-orig (or something like that). Unfortunately in the screenshot above I forget to mark that biq with an arrow in a different colour, but I hope you will find that biq.
4. Now unzip the CCM2.50 files into the C3C mainfolder. The CCM2.50 files will fill up the folders called Art, sounds and Text with the additional files of the CCM2.50 expansion and also add some new files, among them the new conquests main biq, holding the settings of CCM2.50. The folders Art, sounds and Text now are holding the files of the original C3C expansion and the additional files added by CCM2.50.
And one more hint when starting a game:
Your second screenshot shows, that you haven´t activated some features, that should be used when playing CCM: The boxes for diplomatic victory, cultural victory and victory points should be activated, too, by klicking on them. The option of the victory points is needed, that the supply shipments can work.
namayake, good luck with the installation.