You do need an active Internet connection to play OpenLabyrinth cases. We have explored the possibility of creating a player that allows playing of cases offline. In some ways this would not be that difficult. But since most devices are pretty much connected full-time these days, there seems to be less and less demand for this.
If you or your group are interested in collaborating on creating an offline version of OpenLabyrinth, we are still interested in hearing from you. Send us a note through the Support Request pages.