It’s possible that a faulty charger bricked bothe your MacBooks but that doesn’t explain the iPhone…

You have a memory leak somewhere, to be honest you tried everything I can think of except a clean reinstall, so if you can’t find any other fixes, you might want to consider doing that.

Is it only League? If it’s not replace ur battery

Swap out the battery for a new one, it’s hella dead

Almost every single computer will shut down when overheating

Sounds like the cooler isn’t making good contact with the CPU, take it into an Apple Store if you don’t have the tools and knowledge to repair it yourself

If you redownload the EA app it should detect the game automatically

It looks like there’s an obvious burn mark around the component labeled LR5, the resolution however is too low for me to be able to see what blew up

You probably don’t have the tools and expertise to reflash the BIOS, so your next step would be to replace the motherboard or take it into a repair shop and see what they say

If it just shuts down, it’s likely your power supply

Replace the CMOS battery would be a good start