Found at a friend's house.
This 3-way switch is working fine, but it seems to have 2 of the wires permanently bonded together under one screw terminal, with the other one remaining unused. Presumably the red wire on the other side is the traveler (but it's not clear).
According to my friend, any attempt at rewiring this using all three screw terminals results in the other switch only working when this switch is in a particular state.
How is this working? Is there anything wrong with leaving it like this? If so, how can it be fixed?