It should run.

If Simply won't start then Right click on the icon, scroll down to "Properties", choose "Compatibility" tab and select "Run the program in compatibility mode for "Windows XP w SP3"

Do I have to reinstall it, or can I copy over the install folder?

You must reinstall the program!  

It will not work if you just try and copy the program folder to the new Windows 7 computer, besides Windows 7 will probably prevent (or at least complain a lot) if you try to copy files in to the Program Files folder area.  On Windows 7 you data files must not be in the Program Files directory structure

You must reinstall the program!  

It will not work if you just try and copy the program folder to the new Windows 7 computer, besides Windows 7 will probably prevent (or at least complain a lot) if you try to copy files in to the Program Files folder area.  On Windows 7 you data files must not be in the Program Files directory structure