Howdy JayC3D,
How would you be packaging the project (Development or Shipping)? If you are building for development, you would need to have UE4 installed on the Computer as well in order to play you project? Packaging for shipping should allow the project to be played on the computer.
You may also want to zip up the file and then transfer it over that way.
Let me know if this helps with your testing.
Thanks!