This problem is due to a limitation in the app that uses relative paths to define the location of the images. The only way to avoid this problem is to keep MATLAB's working directory as the parent directory of the application's files (where launchEnigma.m resides). We will track this issue on the Git repository and look at submitting an enhancement. Sorry for the inconvenience.
Given the title of this question, I also want to point out that this app was a collaborative effort as spelled out in the File Exchange submission. The development was split between the team of Corey Lagunowich, Cesar Rivadeneyra, Adam Sifounakis, Sean de Wolski and myself.