Okay, just downloaded the demo, aaaand it's the aforementioned 'exe that you click on to run the program not an installer one'.
So, scrap what I said before in 2) and do this instead:
In Crossover, in the menubar, go to Configure: Manage Bottles.
Create a new bottle called whatever you want (a windows XP bottle is fine).
Next, go to Programs: Run Command- a box should pop up.
In 'Use Bottle', select the bottle you just created.
In 'Command', select the AntiqueSoft.exe file, wherever you put it.
Click Run.
The program should then run- I just tried the demoif it does, go back to the Run Command box and click 'Save Command to Programs Menu'
A Finder window should appear after a short while with an app named 'AntiqueSoft', and in the Programs menubar bit of Crossover AntiqueSoft should also be there.
Et voila! There you go.
Edit:
If you don't like it being in full-screen mode, then you can put it into windowed mode:
Go to Manage Bottles again.
Select the AntiqueSoft bottle.
On the right-hand side, go to Control Panel.
In the section below, select 'Wine Configuration'.
Go to 'Graphics' in the window that appears.
Tick 'Emulate a virtual desktop' and enter your desired size.
Click Apply and then OK.
That should make the app run in a window now.
Hope I helped!