In order to test a level, you must have the game supaplex installed on your machine and the path to supaplex.exe or spfix???.exe specified in the supaplex editor options. If those conditions are met, you should be able to test your levels by pressing the Test Level Button (with a Run Icon).
Please note that your operating system must allow supaplex to run (i.e. any Windows version prior to Windows Vista, for example Windows XP with compatibility mode set).
Source: I am the author of the program.