Finally solved it.
I have ms-office running in WINE (all but the sound). Don't use it, but like to show people that it is possible. I took a look at the way WINE set up the menu entries and wrote it down. Then I had WINE install The American Heritage Dictionary to wherever it preferred and wrote down the location. WINE did not, for whatever reason, make a menu entry for the program.
I opened the menu editor and put this on the command line:
env WINEPREFIX="/home/username/.wine" wine "C:\AHDW\AHD3.EXE"
Bingo. It fired right up.
Now, if I could get sound to work in WINE...