Hi everyone, I spent an afternoon figuring this out as a KG player myself, because none of this felt quite right, and I actually stumbled upon the correct answer (or at least, the one that worked most for me). So this is the instructions for people who bought the game legitimately on Kagura Games.
Step 1: Save your saves from the main game to a separate place.
Step 2: (Stay with me on this one) delete the game. You don't have to fully remove it from your computer, moving it to your trash and letting it sit there should be fine.
Step 3: Go to Kagura Games and go to your downloads. Install Country Bumpkin Yutaka as if you were downloading it for the first time.
Step 4: Once you let it install, it will install both the main game and the Gaiden extra content.
Step 5: Move your saves back into the www folder in the real game (if you only see the shortcut, right click and go to "open file location".
If you follow all these steps, you should have both the main game and the add-on, next to one another, and you can click on either one to begin, with the main game having all your saves. If anyone has changes to make in their processes that worked for them, sick. If it doesn't work for you, I apologize, this is simply what worked for me, after working on it off and on from 4pm to 3am.