OOPS! You're talking about adding a game port to your key encoder. The buttons are easy enough - just hook pins 2, 7, 10 and 14 to separate encoder pads and then pin 4 to common encoder GND. That leaves the joysticks, which would need a way to differentiate between ~0, ~50k and ~100k resistance and turn that into 0 or 1 button keypresses... probably requiring some fancy A-to-D conversion and a more involving circuit here than it's worth.
BUT - are you dead set on a sound card? You could just pick one with a gamepad port on the back of it as that would do the translation work for you : )
Also, Microsoft (and maybe others) did the Sidewinder gamepad series a while back that converted button presses to digital signals over the "dumb" analog interface. They were cool because you could daisy-chain four of them together and play over one joy port, though you needed special drivers to interpret the pulses into direction and button presses. I have a couple in my garage, been thinking of a hack with them but it hardly seems worth it since nobody has those ports any more. Of course that's useless now thanks to USB.
EDIT2: Ah I like Boomstick's idea! First you'd modify the gamepad internals to stop them from putting out analog signals and then make them put out digital directional signals (on some of the unused pins). And then you'd add a DB15 connector to your key encoder for the extra inputs. Of course you'd only be able to use your hacked gamepad with your improvised gamepad port but at least it's still an option, and you could do a few this way then allow your gamers their choice of pad. 15 Pins with one reserved for GND would give you 2 directions 3 buttons per pad if you wanted to rig up two...