Mac OS will block you from opening the app since we did not register as developers with Apple yet (unidentified developer simonrepp.com is legit and from us). You can override this in the "System Preferences" of Mac OS in the "Security & Privacy" area where you can click "Open Anyway". You might have to unlock the panel first and then try to open the ZEITMachine again. Be aware that in the popup the "Open" button is actually on the left.
We are still working on the Linux version of this software, please contact us if you want to try it.