Their docs explain how the export works.
If you'd like to share your designs to others that may not have Principle, you can export a standalone Mac app that anyone with a Mac can open. Note: Export for Mac runs on Mac computers, not iPhones. If you'd like to share you're design for iOS, see Running on Device. To export your design for Mac, go to File > Export for Mac. The resulting app can be shared however you'd like, though depending on how you share it, it may help to zip the app before uploading it to a file sharing service or emailing it.
So basically the app will be included in the export you send them, however they will need to have a Mac device.
Alternatively they could use the demo on an iOS device, but they will need to be either connected to your computer or a computer with the Principle App and source file.
Principle Mirror for iOS can be used to view and share your designs on iOS. Download the Principle Mirror app onto your device and connect it to your computer's USB port. Principle for Mac and Principle Mirror will find each other automatically and the top-most Principle document will be sent to your device. In design reviews, press Cmd~ to quickly switch between open Principle documents and the iOS app will switch files as well. The design will continue to run even after disconnecting from USB, making it easy to show teammates.
This is the only way to export the demo to ensure it has it's interactive features at the moment.