The question "how it is that this world is or isn't a "pure land". Presumably the Buddha Sakyamuni has or had a pure land?"
Thanks to your question and the fine answers I understood what "pure land" means. It is what some may call the mind of peace, or the mind that does not vacillate.
Reading SA 557 helps. Do not rely on its Pali counterpart AN 9.37, which has been modified to suit the Pali tradition.
The world according to Buddha is a person's individual experience. How is it brought about? It is done via data that enters through the six entry points, if any of those are touched, that leads to Impure lands. "Touch" has a specific meaning.
If the data enters via these six places without being influenced by the signals the objects emit, then one has found the "Pure land"
An excerpt from SN 35.95
"Not impassioned with forms
— seeing a form with mindfulness firm —
dispassioned in mind,
and doesn't remain fastened there.
While one is seeing a form
— and even experiencing feeling —
it falls away and doesn't accumulate.
Thus one fares mindfully.
Thus not amassing stress,
one is said to be
in the presence of Unbinding"
Right mindfulness most succinctly stated in SN 47. 42 Sutta on Origination or Samudaya, offers us clues as to how to dwell in the pure land.
Based on this discussion "unbinding" in the above verse sounds to me like "Pure Land".
"Pure land" in other words would be a land without defilements, or a consciousness that is un-fastened.
When we begin naming the forms that arise in our minds, that leads to "Impure Lands"?.