You can't directly connect it; you would need some board to convert the digital signals into analog if you want to use them as generic analog joysticks.
If you know how to convert digital to analog, here's the output values that need to be converted into an analog voltage.  Notice the williams 49-way is binary complement of the midway/happs 49-way.
   Sinistar/                       Midway/
Williams 49-way                 Happs 49-way
    1000        full up/right       0111
    1100        2/3 up/right        0011
    1110        1/3 up/right        0001
    0111           center            1000
    0011        1/3 down/left       1100
    0001        2/3 down/left       1110
    0000        full down/left      1111
I guess you could convert it to a binary signal compatable with the digital "analog" joysticks like the sidewinders and all USB joystick, instead of the analog discribed on the page ref'ed.