As per design look like only Green LED will trun on when nLNKA_LED/GIO9 goes low. and when nLNKA_LED/GIO9 goes high no LED will turn on. then how the yellow LED will turn on here?
It won't ever turn on. The supply for the chip is 3.3V so the output will be either 0V or 3.3V. It's effectively the same as if the yellow LED die was not present.
Still better than an eval board I have which has the link LED connected to the power supply through a resistor. You can plug a pencil into the jack and the light still turns on when power is applied.
The schema doesn't make sense, from what I have seen as common practice.
The only way I can think of is that "nLNKA_LED/GPIO9" is either 0 volt or 6,6 volt. That way the current will either flow through the green or the yellow LED.
A common practice when you have two LED's in opposing directions, you normally have two I/O pin connected to either side.
This way you can have either the green or the yellow lit with just two wires.
The way you do it is:
Pin 9 Pin 10 LED lit 0 0 No light 1 0 Green 0 1 Yellow 1 1 No light