Good question; after using a standard lighting controller to capture cues or recordings you can command the CueCore to start or stop playback of this data.
Actually there are several ways to control the playback: via DMX, Art-Net, MIDI, OSC and UDP. In the 'Show control' webpage you can set any of these protocols to trigger cues or recordings.
So if you are making your software system you can pick any of these protocols, which ever you feel most comfortable with. I would definitely consider OSC because it is a beautiful protocol for these kind of applications.