If Plant Tycoon wanted you to be able to open .ldw files directly, when the program installed itself it would have registered the .ldw suffix with windows so that windows would know what program to use to open them.

So that is why you get the message about "what program do you want to use to open it with". You could of course open the list of programs and browse to programfiles\planttycoon and use plant tycoon.exe to open the file. However, that won't really work. All that will do is start plant tycoon. Plant tycoon won't play the file you selected, it will play the last game you played in plant tycoon, as it always does. And manually registering .ldw files with windows as "Plant Tycoon" files is not a good idea anyway, as the .ldw suffix is used for other ldw games, not just plant tycoon.

Knowledge is a good thing so I will close with some of that. Here is a run down of the save game file names in your Plant Tycoon save game folder:
Plant Tycoon0.ldw - this is not a game but rather think of it as a table of contents of sorts that lists information about your plant tycoon games. information such as name of game and which game you are currently playing, etc.
Plant Tycoon1.ldw - this is the plant tycoon game you have in game slot 1.
Plant Tycoon2.ldw - this is the plant tycoon game you have in game slot 2.
Plant Tycoon3.ldw - this is the plant tycoon game you have in game slot 3.
Plant Tycoon4.ldw - this is the plant tycoon game you have in game slot 4.
etc.
There is also a log file which is a text based file that you can open in wordpad or whatever your favorite word processor is. Read it one day if you are bored.

Have a really nice day,
-Borg