TI TPS6116 Output Voltage
Am I missing something?


The TPS61161 can produce a maximum of 38 volts but its main aim is to provide a constant current for any LEDs connected. It does this by monitoring the current through \$R_{set}\$ below: -



In effect, the duty cycle of the TPS61161 is adjusted to force the required current through \$R_{set}\$ and whatever the peak voltage is at the top LED anode is whatever it needs to be to supply current through the LED string. 

The FB pin needs to reach 200 mV and then the chip regulates so, in the circuit above, if 20 mA flows through the LEDs and \$R_{set}\$ is 10 ohms then 200 mV is produced at the FB pin and, the chip regulates that voltage by continually adjusting the duty cycle to maintain 20 mA through the LEDs.


  The backlight in question requires 12.8V.


The devil is in the detail so, without any other knowledge about the LED in question, it's impossible to say if the chip and its circuit is suitable.