Android - Can I use my phone as a bluetooth game controller for my computer?

There are a bunch of apps available on the market. Some examples include...

• BT Controller: "BT Controller allows you to use your android device as a gamepad controller for any other android device." (well, you already saw this)
• Bluetooth Remote PC: "Bluetooth Remote PC is an app which allow you to remotely control your PC. Get access to the computer and use your favourite programs from distance. You can control mouse, keyboard, multimedia, presentation or power system commands."
• PC Remote Controller (doesn't use Bluetooth, but rather WiFi)
• BlueControl looks like exactly matching your request: "Blue Control is a basic universal Remote Control for Blue-Tooth enabled serial devices such as Blue Tooth modules connected to a micro-controller. For each button pressed the corresponding ASCII code for the label will be sent. For example pressing buttons A-H will send the charactes "a" - "h". The up, down, left, right, and center buttons will send "U","D","L","R", and "C" characters. Hopefully this will inspire people to create alot of fun Blue-Tooth Controlled devices."

A lot more Remote-Control apps can be found e.g. in this listing at AndroidPIT (Google translated) (original link). Though descriptions are in German, the general groupings and items should be recognizable ;)

You haven't mentioned which types of games you need this for but there are several possible options:

Gmote 2.0, which is a client/server type system which would let you use your Android tablet to control your computer.

RemoteDroid, which is similar to Gmote, it also uses a client/server system.

GRemotePro may be the right choice for you as it is but you need to pay for the server software. It is specifically advertised as being for game control.

nJoy is a very good app as well, it uses WiFi but you can just use your own hotspot if you're not using WiFi atm and turn off data if you don't want extra charges.