I'm going to assume "relatively high level languages" are for example Python, Ruby, C#, Javascript...
Imagine that you have your high level program. When you execute it, it goes through a just-in-time compilation (whether that's script parsing or bytecode conversion, or actual compilation, or whatever) before reaching the CPU which actually executes your code. Now imagine that your interpreter has the capability of reading and monitoring everything you do.
Nothing wrong with that, it's supposed to do that, it's how it works. But imagine if it had an exposed, unlogged, unmonitored, API which allowed a third party to be able to interact with whatever you do. Say that it's there "for debugging purposes".
You want to encrypt an HTTPS session? This API allows them to grab your key without ever notifying you. Or, even if you use custom encryption, it allows them to grab your specific instructions and the data used in processing to reverse your encryption.
It allows a remote party to inject their own flow of execution into your program. So you're sitting there waiting for the next user event to occur in your event loop while, instead, the interpreter simply handed the whole event loop to a third party. They could inject user events for you to process that the user never actually performed; they could modify data in ways that you can never detect.
Except that it's not the interpreter. It's a side-channel, an additional hidden core on your CPU (it's actually a completely hidden and separate secondary CPU). Your processor still runs and executes your code. But another processor is simultaneously running and executing its own code with its own RAM that you can't access. It has access to your RAM as if it were a file open on your hard disk.
You can't disable it. You can't interact with it. It's even running when your computer is "shut off". If there's power on the motherboard, then this hidden processor is running.
That, in a nutshell, is Intel ME...
... This sounds _really_ paranoid and alarmist. But it's not all bad. Intel has usually done really well with "security through obscurity" in this case and there aren't many known exploits for Intel ME. That said, those that do or could exist, gain all of the capabilities of Intel ME.
Most people consider "game over" for physical access anyway, so I'm not sure that pwning it with physical access is a new problem; instead it's a secret basement in a bank; it's only a problem if someone figures out it's there and starts digging a tunnel to it.
Also, remember that a lot of motherboards these days come with built-in wifi or bluetooth adaptors. Intel ME has access to those too; you can't just rely on an upstream firewall for your physical ethernet. With the right (wrong?) exploit, all it takes is an adversary to be within directional antenna distance (which is actually really far) to be able to pwn your system. The best way to prevent abuse over that channel is to physically break the antenna connection (lol warranty voided because you've damaged your motherboard).