The author is correct when he says these are Android-BASED phones. Like pretty much all the Android-based phones out there (with the exception of Google Editions and the Nexus devices) are like that, most of them are also certified by Google (meaning access to Google Apps and Play), whereas a few don't meet the requirements and are limited in terms of the apps availability. That being said, I expect these phones to have full access to Amazon Appstore, which contains pretty much all the apps from GPlay (except for GApps, of course, but these can be easily replaced with equivalent apps from Playstore).
Since Android is a linux based open sourced OS, it is available to any manufacturer, who in turn can modify it to it's liking. Some out there are pretty succesfull at that (HTC, Samsung, Huawei, Sony etc) while a few obscure ones choose to heavily modify it.
This correct distinction is seldom encountered on so-called tech sites (this one is usually no exception), but even when outlined correctly, it is still glanced over by readers (they stop reading at Android and ignore the BASED part) and in turn feeds some ubiquitous [ignorant] trolls on said websites.