When you start a 3D application (most modern games) the graphics card need to work harder compared to 2D (desktop). The result is that both the PSU and GPU becomes warmer and if the component has a temp controlled fan, it will spin faster to combat the rising temperature.
Since the GPU becomes a lot warmer compared to the PSU, its likely the cause of the annoying sound. You can easily test this by placing your finger at the middle of the GPU fan (don't insert it into the blades, it can damage the fan and hurt your finger) also be gentle (don't damage the fan) when you place your finger at the middle of the fan so that it slows down and then stops. If the sound goes away then its that fan that is the cause. If the sound remains then its likely another fan and you can test them the same way as long as you can reach and place your finger at the middle of it. Do NOT open the PSU and put your fingers anywhere inside there.
Once you have identified the faulty fan, return it to the place of purchace for a replacement if you have warranty. Otherwise you may need to look at a replacement solution. If its a custom fan/cooling solution like for GPU or chipset on motherboard then they will most likely replace the whole product (if in warranty). Out of warranty a 3'rd party solution is almost always needed.