Missing on Lost Island

Lost Island is a German 3rd POV point-and-click adventure game with English dialogues and subtitles.

Tim and Diana, walking home at night, meet a couple of men dressed like 17th century pirates who are loading something on a cart. Disturbed by the couple, a man with a wooden leg shoots Diana with a laser gun and she vanishes. In the fight Tim is also shot and disappears as well, and materializes naked in a deep crater, somewhere in a different time period. Before you are on your way to find Diana and return to your own time and place, you have to find some clothing and find a way to get out of the pit.