Parallel led segment with (1 led) and (2 led in serie) without resistor?
Its possible, but why they did this is hard to say. (if in fact this is the actual diagram, it is a one color LED so this could be correct). If the diagram is drawn correctly, at a lower voltage only the red LED will conduct and the two in series will be off. At a higher voltage all three will be on but the LED that is not in series will be getting more current. Since nothing else is known about the LED's (no voltage, color, or IV curve) nothing can be said of the actual operation.

This may make more sense if the LED's were two different colors. 

If you use this you'll need to provide current limiting with a circuit or resistor. 

You could find the IV curve but increasing the current in steps and measuring the voltage,and that would tell you more about this terribly undocumented product.