Adobe Illustrator used to have an Effect → Warp tool called Crystallize, that was good for creating starburst shapes & effects, like this:
It seems to have disappeared in the last few years (actually, sometime between 2015 & 2018). There’s a totally different tool by the same name (Effect → Pixelate → Crystallize). There’s also a similar, but slightly different tool with a different name (Effect → Distort & Transform → Zig Zag). There’s also the Star shape tool. But none of them are quite the same.
What happened to it? Has the name changed?
Has it been removed? If so, how best might I emulate it?
Nothing happened, it was never an effect*, just a tool.
You can access it by holding down on the Width Tool and switching to the Crystallize Tool
To access the adjustments, double click on the tool (once activated).
Let’s look at adjusting the button for this tool. If you double click on the Crystallize Tool button you will get the Crystallize Tool Option window.
To make sure you are centered in the shape, just make sure to have Smart Guides on (Ctrl+U to toggle on/off) and then you will snap to the center point.
*This is in my CS6 version of Illustrator (2012). The article you linked makes no mention of an effect, only the tool.