Apart from the requirement to use the "Calibrate Joystick" option in the menu before trying to use the device (even on a Windows machine), there don't seem to be any limitations listed in the printed documentation.

If your motherboard has an on-board gameport, you might consider making sure it is turned off in the BIOS or try to use it instead of your soundcard gameport.

When I try to calibrate, it says no joystick is detected. For now I'm using the onboard gameport since the sound card I ordered hasn't arrived yet. Is it possible that the game is not compatible with onboard gameports, but will work when I disable that and install an ISA sound card w/gameport?

Well, anything is possible.

It might be helpful if you indicated exactly what controller you are using. Perhaps someone who owns one like it will be able to give some information about problematic games or circumstances.

One thing that might be worth checking is what resources your motherboard is currently using for the gameport. Even if the game documentation doesn't list them specifically, the game may be looking for particular values to be used for a given resource type. For example, I have played the game on one machine of mine that has a Creative Sound Blaster Live! (CT4760) that is set to use the following resources in the SB16 Emulation:

SB Port: 220
MPU 401 Port: 330
ADLIB Port: 388
IRQ: 5
8-bit DMA: 1
16-bit DMA: 5

These are fairly "safe" values that are acceptable in most DOS games.

Edit: I left out the most important value (sorry):
Gameport I/O: 0200-0207

is your joystick working within windows joystick control panel applet ?
is it working in dos. download and run joytest.exe
http://www.epanorama.net/documents/joystick/pc_joystick.html

ps: it does work in your other games ?