The game ran just fine but didn't recognize my wireless Microsoft Xbox360 controller. I couldn't find a solution in the Steam forums but after a short Google search I found a working solution in the Ubisoft forums. The solution isn't mine but I can confirm that it works like a charm!

Each game controller or game pad produced has its own "product ID" or 'PID'
The problem is that the controller game is looking for has the wrong PID.

You need to go into the config file and change it.
This may seem daunting, but it is really very easy.

Open the folder into which Steam has installed the game and go to the folder called "Kellergame", then open the "Config" folder and finally the "PC" folder. There is also a file called PCKellerJoysticks in the Config folder but changing that won't help!!

Open the file "PCKellerJoysticks" (u can just double click on it and it will open in notepad as a text file)

The top few lines will read:
[Joystick0]
ProductName=XBox Controller HID Minidriver, XID
VendorID=***some number (a)**
ProductID=***some number (b)**
Joy1=XboxTypeS_A
Joy2=XboxTypeS_B
Joy3=XboxTypeS_X
Joy4=XboxTypeS_Y

you have to change (a) to 1118.

Now, you need to find out what your Product ID is. Before that though, two very likely IDs are :673, and 1817, so try each of those first.
(to check them, change the number, save the file, and then run the game and try to turn on the "use 360 controller" option in the game.)

If neither of those work, you will have to find out what your PID is manually.

Go to Device manager and under "Human Interface Devices" there will be your game controller. (if they also appear under "universal serial bus controllers")

right click on your controller and chose "properties"
In the window that appears select the details tab. Go to tje drop-down menu and choose "Hardware Ids"

In the "values" box you will see something that looks like this:

HID\VID_045E&PID_0719&IG_00
HID_DEVICE_SYSTEM_GAME
HID_DEVICE_UP:0001_U:0005
HID_DEVICE

Those are the ID's of your controller.
(Do not worry if your values are slightly different.)

What we will focus on is the first line at the top (HID\VID_045E&PID_0719&IG_00)

Let me translate: Human Interface Device (HID)\Vendor ID(VID) 045E (the number 1118 in hexadecimal) & Product ID (PID)**YOUR PRODUCT ID** and then the rest doesn't matter.

What you are looking for is the PID. (mine is 0719)

BUT WAIT!
That number is in hexadeximal digits. Google "hexadecimal converter" or something along the line of that, and convert what your PID is into deciaml digits.

TA DA!
You now have your product ID so that you can go into the PCKellerJoysticks file and change (b) to your PID

Although the controller will now work with the game, the controls might be screwy, so you need to add this line in : "UseXInput=true"

Mine now looks like this:

[Joystick0]
ProductName=XBox Controller HID Minidriver, XID
VendorID=1118
ProductID=1817
UseXInput=true
Joy1=XboxTypeS_A
Joy2=XboxTypeS_B
Joy3=XboxTypeS_X
Joy4=XboxTypeS_Y
Joy5=XboxTypeS_RightShoulder
Joy6=XboxTypeS_LeftShoulder
Joy7=XboxTypeS_LeftThumbstick
Joy8=XboxTypeS_RightThumbstick
Joy9=XboxTypeS_Start
Joy10=XboxTypeS_Back
Joy11=
Joy12=
Joy13=
Joy14=
Joy15=
Joy16=
Axis_X=XboxTypeS_LeftX
Axis_Y=XboxTypeS_LeftY
Axis_Z=XboxTypeS_RightX
Axis_Rotation_X=
Axis_Rotation_Y=
Axis_Rotation_Z=XboxTypeS_RightY
Slider_0=XboxTypeS_RightTrigger
Slider_1=XboxTypeS_LeftTrigger
DPadUp=XboxTypeS_DPad_Up
DPadDown=XboxTypeS_DPad_Down
DPadLeft=XboxTypeS_DPad_Left
DPadRight=XboxTypeS_DPad_Right

I didn't come up with this solution myself, but found it on the Ubisoft forums (of Rainbow Six: Vegas 2) so this fix should work for that game as well.
Thanks to jg_guy and sprinkill1980 (who pointed out that you have to go to the PC subfolder) .