Both the miller and atkinson cycles have modified timing but are still considered to be 4 stroke engines. Atkinson with the exhaust timing and Miller with the intake. The piston still only moves up and down 4 times per cycle or 2 if its a modified 2 stroke.
Now this then depends on how you classify stroke, does a secondary intake on the miller cycle count as anther stroke, or does it count at just count at having a very long intake cycle that overlaps to comprression. The answer is up for debate really but both Atkinson and Miller still only have 4 stages to the cycle.
Intake Compression Power Exhaust.
You can break down those stages to magic up more stokes, the standard thinking is that although it has a two stage intake the second is a 'pseudo stroke' if you will.EDIT: Just look at the quote you posted. the word fifth is in inverted commas and has the words 'so called' in front of it. Also just read the first line of that wiki entry.
"In engineering, the Miller cycle is a combustion process used in a type of four-stroke internal combustion engine"
As much as wiki is an unreliable source of information, its bang on with that one.6 strokes have 6 discreet cycles.
Intake, Compression, Power, Exhaust, Steam/Air Cycle, Steam/Air Exhaust.