This is a explanation on how to make Dwarfheim function. This is from what I understand only fixes the game into a singleplayer state where you can get passed the account check. Since the game is abandonware.

Step 1: Run Dwarfheim for the first time then close the game.

Step 2:
Go to this Github page:
https://github.com/SuiMachine/DwarfHeim---Project-Rebellion

Step 3: Download 2 .zip files from the page:
BepInEx UnityMono x64 6.x
Sui's Hack

Step 4: Open both zip files. BepinEx should have a couple items and Sui's should have a couple items. Extract both folders into your Dwarfheim Directory and or wherever the Dwarfheim folder is located. Mine is in the Steamapps folder.
This is a little confusing for some because when you actually look in the Dwarfheim file in your steamapps it will have a standalone folder called client. Client is actually the directory folder.

Step 5: Run Dwarfheim. Should be able to run all the modes in singleplayer. Enjoy.

Credits: Thanks to Sui for the fix to the game we all love. <3