I didn't ignore the alternatives. I specifically stated that MS controlled 95% of the world market at the time (1999 -
https://time.com/3553242/microsoft-monopoly/ ). I then stated that there were "literally" no alternatives. There were 113.5 million PC sold in 1999 (
https://www.latimes.com/archives/la-xpm-2000-jan-24-fi-57038-story.html). Of that total 111.5 million were running microsoft software and Apple sold a measly 2 million units for a 3.4% market share (
https://igotoffer.com/apple/history-apple-1999 - scroll to the bottom for the numbers) and had virtually no presence in the business world. That's a textbook definition of a monopoly and support for the true statement that there were "literally" no alternatives to MS in 1999.
What you are arguing is that Apple is a monopoly simply because it exerts total control over it product. That is not the standard and accepted legal meaning of a monopoly. In fact, if you are trying to make the case that an OS has a monopoly in mobile phones it would be much easier to make that claim if you referred to Android which has a 75% market worldwide (
https://www.businessofapps.com/data/android-statistics/ ). Your argument also completely ignores the fact that in regards to gaming there are a myriad pf platforms (playstation, x-box, google play, steam etc) where games like Fortnight can be played. Again, from a market share perspective, Apple clearly doesn't have a monopoly.
Your definition of a monopoly would make virtually any business a monopoly. Every gas company (Shell, Exxon etc) would constitute a monopoly under your definition because at their gas stations they have total control of what they sell and you can't buy another brand of gas from them or use your Exxon points card at a Shell station. Netflix, Hulu, HBO etc would all be monopolies because they control their content, pricing and have exclusive content not available elsewhere. And the list goes on and on.
If you don't like Apple's control of their ecosystem that's fine don't buy from them...you have other options. And its because you have those options, and because Apple is not the dominant market player in any area it competes in globally, that unfortunately no matter how hard you try you can't call the App Store a monopoly (no matter how much you want to).