Is the older macOS's a GPU killer?

I’m a bit confused on your questions:

The dedicated GPU in any mini is not throttled.

But! The CPU can be when the system overheats because the fan, heatsink or the sensors have failed. This is often a symptom the system has dust build up within the fan and logic board, I would recommend installing a good thermal monitoring app like TG Pro. Post a snapshot of the main window so we can see what you are encountering here Adicionar imagens a uma pergunta já existente.

You can alter the display settings choosing a lower resolution if you want to lower the GPU’s processing load. You can also alter Safari site by site as well altering the page to reader mode.

The 2012 model as well as the 2014 models use a different logic board design and the logic board is not the same. Even that won’t alter the limits of the systems cooling. In fact from what was seen in the new 2018 Mac Mini presentation it looks like Apple made a big effort finally addressing the systems limited cooling.

So the bottom line here is Your system likely needs a good cleaning and needs the thermal paste refreshed at a minimum. You may need to replace the heat sink and you likely need to look at lowering the systems heat buildup like swapping out the HDD for a SSD as well as look at upgrading the RAM (16 GB max).

Do remember MacBook laptops (all) and the mini are not gaming rigs! If you want that, you’ll need a system with much better cooling.