There are a few different steps in order for this to work on Steam Deck, here they are below.

Before we start, make sure you have installed the game on Steam before beginning.

(1.) If you are in Gaming Mode, hold the power button until a menu appears. On this menu, Switch to Desktop mode and follow the instructions in your browser of choice here: https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2265283307 in order to download the patch. (Register at Kagura Games, add the patch to your cart for free, then download it)

(2.) You will find that the Patch application does not run on Steam Deck. In order to make it run, go to your Discover store (Blue icon at the bottom left of your Desktop) then search for and install an application called "q4wine". Let it install with its default settings, we dont need to mess with anything on q4wine.

(3.) The Patch application will now run through q4wine, however the patcher cannot properly target our game folder in its current location ('primary' on Steam Deck). So we are going to temporarily make our game files reachable.
Create a new folder on your desktop (im going to call it GAME folder)

(4.) Open Steam (still in Desktop mode) and find Succubus Affection in your library. Click on the 'Manage' gear wheel on the right side of your screen and select Manage>Browse local files. This should open our game folder with the files we need to move.

(5.) Now that we can see our game files, we need to pull them out of the primary partition and put them in a place where our Patcher can see them. CUT every file and folder from this directory, and PASTE it into our GAME folder which we made on the Desktop.

(6.) Now that our game files are accessible, run the Patcher with q4wine, and when asked for our game directory, use our GAME folder we created on the Desktop. Viola! The patcher should now properly update our game. Wait until this is finished.

(7.) When the Patcher is done, we can now CUT the Updated game files, and PASTE them back where they came from in our primary partition. If you cant remember where to PASTE, repeat step 4 to find the correct directory.

You can now go back to Steam Deck 'Gaming Mode' and run the game as normal. Congrats! You are now running the updated version.
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Hope this helps, and if anybody is struggling with those instructions let me know and i will try to simplify them and update this guide.