That's the answer, full stop. Like it or not, the rules are different for you when you have the majority of market share, and this has been true in both the EU and the US despite their different approaches to antitrust regulation.
I guess that the issue is that I am not as much against Google using Android to distribute its services (I would be using most of them anyway and those that I don't use (newsstand, spaces, ..) can be replaced anyway) but against being unable to distribute/install whatever software I want on a general purpose computing device.
And AFAIK, sadly there is no law governing this.
The argument hinges on Google not owning or operating Android. AOSP has been a dead dream for a while now due to carriers locking down phones and Google needing to circle the wagons.
As you mention, AOSP alone does not give you much Android and Google is likely to dictate all kinds of terms to use the Play services, Play Store, etc. So, the question is indeed does AOSP give enough to argue that Google does not fully control the Android market.
Personally, I am not sure this is the most problematic aspect of Android though. If we assume for a moment that Android is a near-monopoly in the EU, the more troubling aspect is that people can only choose between having no smartphone (which is becoming harder) or letting Google suck all kinds of data out of them. In other words, only when you are rich enough, you can afford not to let a company suck up a lot of your private data.
There are still a couple of european countries where iOS devices sell extremely poorly. I am not sure if this is because of an absence of subsidies or another reason.
Even if Android is the only option, you can always choose to refuse all data sharing from google, you are not forced to create a google account or to use google play.
Admittedly, it makes things harder for a neophyte.
That's only in the US.
Let's be honest here, AOSP is a dead dream because porting and maintaining AOSP for a device is kinda complicated. Many people do it for free, but you can't rely on that.
GPS includes stuff like location services, Firebase, Chromecast, analytics, Google account authentication, Google Drive APIs, all the game stuff, Android Pay, etc.
Or which things can monopolistic companies do that non-monopolistic companies can't do? Can or do Apple do those things?
Which practices a monopolistic company can do, but is not allowed to, is written clearly in the article: Forcing/Paying other companies to pre-install its proprietary apps. A non-monopolistic company is allowed to do that.
My local corner shop has a market share of 100% of the places I can buy things if I walk 30 seconds but that's hardly relevant when I can drive 10-15 minutes and have 4 different supermarkets at my disposal.
That's not relevant in the phone market, where you're stuck with a specific platform once you've made your initial phone purchase. You can't use it with applications from other platforms, and switching platforms means you need to purchase all the stuff you're using all over again.
Although usually when I hear people misuse antitrust concepts on tech forums, they're not trying to understand complicated legal conflicts, rather they're grasping at straws to use as ammunition in dumb flamewars about platforms/companies/etc. that they don't like.