I don't think that's possible to download the Walgreens PhotoShow Express or any of the photo shows that you've created. From what I see, the software didn't have the option to upload the files to a cloud to be able to download them to your PC.
You should focus on other applications that have a way to saving your content to online video hosting sites. A good example is the following application called ProShow Producer. The application allows you to create photo shows that you can upload to Video (while keeping them private) or other hosting websites. You can even make copies of the output files and stored them into a cloud service (eg. Google Drive).