This guide was made for a PS4 controller, but should work for any gamepad with analogue sticks.
This guide changes the way Steam registers analogue stick inputs so that diagonals will properly register. If you insist on using a D-Pad, then get good or maybe consider using a keyboard.

Okay, so before we can modify your controllers configuration,
we have to Enable Controller Configuration.
Once your controller is plugged in, open up Steam and navigate to the upper left. Select Steam, then select Settings
You should now see a menu like this, select Controller, then General Controller Settings

Now you can Enable Controller Configuration. put a checkbox next to the controller you are using.


You can exit out of this menu now.
Go to your Game Library by selecting Library at the top of the screen.
Your game list will appear as a list along the left side of the screen.
Right-click Them's Fightin' Herds and select Edit Steam Controller Configuration


Here's what the menu should look like, it may vary slightly depending on what controller you are using.


Once in this menu, click the box for the left analogue stick, we're gonna modify it's settings.


You should see a menu like this, titled Style of Input. Make sure that the style of input is set to Joystick Move, and the output is for Left Joystick.


Navigate to the bottom right and select Additional Settings


Last step, select Deadzone Shape and set it to Square.
There are additional settings here that you can experiment with, but I find the default settings adequate.


Press escape to exit this menu. Now when you start the game, enter training mode and try out the improved controls. You should find it much easier to land those diagonal inputs and execute special moves that use diagonal inputs.