That circuit looks like a NAND gate to me - so the transistor will be on if both inputs are high, but off when any of them are low.
If the transistor is on, it will pull the output down to ground, hence the NAND function.
If you connected your LED with the anode (through a resistor) to VCC and cathode to the output, it would light when both inputs are high. Alternatively, you could add a second transistor stage to act as an inverter.