FWIW, I've spent a huge chunk of time studying ethics on my own. It's true that I can't claim to know a LOT of history about antitrust law. But the reason it's possible to make sense of "complex systems" is the use of (correct) principles about how they work, not examining every concrete example ad infinitum and saying, for example, "well, but maybe the ball will fall up next time". Anyway, putting aside the philosophisizing, I have more specific comments below.

It's illegal when I use my monopoly to stop competitors from selling their own widgets

My point is that your only means to do that is to use government force, i.e., laws. (Now there's a principle for you!)

Now, I might obfuscate the design of my widgets so that only I can make other widgets that interface with them. But that's not the same thing. For example, that doesn't stop others from making their own entirely separate system of interconnecting widgets. Similarly, Apple controlling what's in the App Store doesn't stop Google from creating it's own app store and controlling it's content. One might say that Apple "has a monopoly on content of the App Store," but that's using the term "monopoly" disingenuously.

This is not supposed to be a complete proof of anything, but it's supposed to suggest my line of thinking.

If you believe that this situation is impossible, then the law is irrelevant

Quite the opposite. The law is highly relevant because it's what makes the "cheating" possible. For example, if Apple got the government to bad the Google Store. Or if the EU bans Microsoft tightly bundling IE in Windows, for a real example.

You are mistaken.