The watts aren't the key the 12v rail is
The ATX 2.x spec requires that PSUs be able to provide at least 80% of their total output rating on the 12V rail so the power rating on any self-respecting vendor or manufacturer's PSUs will be a fair representation of their 12V rating.
The HD7770 does not "need" 500W, 500W is merely what the manufacturer feels comfortable recommending for the whole system based on the fact that they have absolutely no clue how good your PSU is nor how power-hungry the rest of your PC is. The GPU itself only requires 80-100W, half the claimed 19A requirement on 12V, indicating that this 19A figure most likely includes 9-10A for the CPU.
Just shows how much "requirements" on GPUs can be total hogwash. Manufacturers are making PSU selection more confusing than it needs to be by lumping system-wide assumptions in their requirements/recommendations.