The demos don't support joysticks; you'll need some sort of keyboard emulation software to do so.
The retail game does support joysticks, though it's not obvious. Here's the joystick section of my autoexec.cfg:
//Joystick Settings
seta in_joystick "1"
seta joy_threshold ".3"
seta cl_run "1"
//Trackball Settings
seta in_mouse "1"
seta m_side "0.25"
seta m_forward "0.25"
seta m_yaw "0.022"
seta m_pitch "-0.022000"
seta sensitivity "30"
seta freelook "1"
//Axis Bindings
bind UPARROW "+forward"
bind DOWNARROW "+back"
bind LEFTARROW "+moveleft"
bind RIGHTARROW "+moveright"
//Comment
echo "CH F-16 FighterStick + KEMP loaded"