My first impression would be that it is not A. parryi because a) more pronounced that expected mammillate margins - teeth on almost all parryi's are not set on pronounced 'teats', b) for the plant's size it has too few leaves, and c) the leaves are bending/curling over outward which I do not think I have ever seen on a parryi, they tend to keep their leaves in a more stiff upright fashion.
Now the caveat to points b and c is that plant growth form and behavior can distinctly change based on growing conditions. Living in Arizona I mostly see plants that grow in their natural habitat or in situations very close to it. More light poor, generally cooler, and/or more humid conditions may have a distinct effect on the plant's form.
That said I feel that the link the photo poster provides shows two distinct plant pictures where I am suspicious that the first picture - which is the main picture - shown is also not actually A. parryi, the second looks more like a typical A. parryi.
But when plants are relatively young and grown out of ideal habitat and the ID is lost, it becomes really hard to say what it then would be - much easier to say what it does not look like. Also if it was seed grown there is always the option that it is a hybrid of some sort. So from my perspective while it being an A. parryi or a hybrid with that plant is not impossible, I do not think so. So posting it in the generic Agave entry seems like the best way forward.
