The properties pattern is especially useful (or, it has been for me), when your want to make prototypes of objects or have a development structure that somewhat forces you to have an iterative deployment of your API/Interfaces.
If you start out with an idea of some properties of an object, then you make them. Later on you find (and you have anticipated this finding...) that your understanding of the subject area was not adequate, you make a new object design/behavior based on the prototype of the first object. And so forth. The wiki-page on the subject has a very good description of the subject in conjunction with static typed languages, but I would recommend that you looked into JavaScript or Lua if you're really serious with prototyping development. The properties of prototypes are not mutable in the static typed languages, and this fact will eventually bite you down the road.
Edit: Oh, and I see you link to an excellent post on the subject. Yegges use/explanation of the subject of course does dwarf my own. Please read it through a couple of times and the advantages/implications of the use of the properties pattern in a language like java should be very clear to you.
Edit.2: link to wikipedia article: http://en.wikipedia.org/wiki/Prototype_pattern