Buzzing noise coming from inside the computer while playing games

If it's the regular types of pc beep patterns, you can reference the motherboard manual to tell what problem it is trying to communicate. But i suspect that is not the case.

What you describe almost certainly translates into those indecipherable buzzing sounds that suggest the state when the audio hardware is getting rubbish input signals - due to the hardware crash - and thus producing rubbish noises. This does not necessarily suggest the audio hardware to be the faulty component; it can be any combination of components, unfortunately.

In my historical case, it was simply a bad combo of processor + motherboard. Not video card, not audio card, not RAM. I was only able to finally diagnose this with a second computer to swap parts individually. Using the processor on another motherboard, and the motherboard with another processor, worked perfectly stable.

You'd have to slowly troubleshoot a component at a time.

I would recommend figuring out what is making the buzzing sound for starters. The most likely cause for buzzing would be the fans but as you've said, you don't think that is the case.

If the sound relates to electrical buzzing, the likely source is the Power Supply (PSU) coils. I currently have a similar intermittent problem involving coil whine which is however more whine than buzz. Where coil whine tends to be higher in pitch than what you're describing hence I don't think that's what you have.

There is a chance that something is shorting (and therefore arcing) somewhere in your computer. If you see any sparks, the part should be sent with great haste for repair or simply binned.

Having just listened to the recording, this does not sound like anything electrical, nor does it sound like coil whine. If my ears are not mistaken, that is a fan. There could be a piece of plastic in a fan somewhere, something like a zip tie perhaps? Since it's intermittent, the offending fan may be on a temperature switch (it turns on when it gets too hot). Your main hardware is very good so it's unlikely to be that, I would check motherboard fans or other little fans that can be dotted around various components. The PSU fan is the likeliest cause.

EDIT (noise located in Graphics Card)

Look for things caught in the fan blades, or at the edges of the blades. If that turns up empty, and the card is under warranty, I would return it. If the card is no longer under warranty and you have the technical know how, you can attempt to locate the problem yourself by pulling apart the card. One of the fans themselves may be buzzing in which case you could try to replace it or just unplug it.

By the looks of it, your card is sagging in it's slot a great deal. This is likely what's causing the problem. For starters, you can try lying the case on it's back (such that the motherboard is facing up) which would decrease the strain on the GPU case. If this works to stop the buzzing, you are going to need to find a way to support the gpu. These usually do the trick: AMAZON