GPUs are just like CPUs. Static electricity, or electricity in the wrong place and you fry the entire thing.
Copy & paste title lol.
More often then not the thermal compound or thermal paste will seep out from the die and go onto the PCB. Non-conductive pastes/compounds (which are mostly all of them at least for PC building) stop the paste from creating a closed circuit between two soldering joints or pins, thus short circuiting the GPU.
Nonconductive refers to the paste being not electrically conductive. This is beneficial on GPUs because GPUs have bare dies meaning the silicon die and any passive components mounted on the top of the GPU package are exposed, not protected by any heat spreader. The reason you don't want electrically conductive compound is because any seepage off the die will come in contact with the passive components surrounding the die and short circuit them together causing the GPU to malfunction or even be destroyed.
the real reason is that the under ground reptile overlords demand that we use non conductive thermal paste on the gpus because the conductive thermal paste is poisonous to their young that live among us.