The one you linked to is for DIPLOMACY.
Notice how it says after the link for it: 1. Updated to Diplomacy version 1.37
You don't want that one.
If you go to the top of the downloads page you will see the very first download that is listed says:
[ Core Mod ]
( 12/24/2013 )
From: DS Team
Updated By: rjhughes67
For: Rebellion v1.80 + DLC's
..... v0.21R+FWSP-RG Change Log.....
1. Removed Sol System Planets and Star reducing core mod by 200mb
2. Added DS Flagship meshes and some abilities to core mod
3. New UI to give DS a new fresh look
4. Changed faction selection screen to now show DS player portraits
5. Fixed player window file to read all 19 sets of portraits not 18
6. Removed Star meshes as Rebellion ones have hard point for particle effect
7. Reset all star gravity wells to stock Rebellion sizes
8. Removed double entries in the entity manifest
9. Removed unused strings from the string file
10. Fixedsome planets referencing incorrect mesh resulting in odd looking textures
11. Ryat's Balancing and Abilities
Notice how that one says For: Rebellion v1.80 + DLC's?
Yeah, you want that one. It's for Rebellion 1.80. And the DLC's if you have them.