We are both responding to: "I love my iPhone but I really don't get this. Apple only has 31% of the smartphone market and Android has 59%, for example." and in turn the original article
In this context the interesting definition of 'market share' is the one that focuses on platforms. There isn't very much interesting to be gleaned by making the distinction that Apple has a bigger market share than Samsung as Samsung and other Android OEMs collectively benefit from Android's market share.
No, because the article essentially asks: does the new iPhone have enough bells and whistles to keep it's position, and compares it to other handsets like Nokia Lumia and Galaxy Note. It's putting up iPhone 5's hardware features against a few competing phones. It does not take platforms, operating system or any software into account.