For the abstractionist, possible worlds don't (necessarily) have the properties they represent certain possibilities as having--- they merely represent.
If you're a concretist, like David Lewis, you can claim that a possible world represents a certain possibility by simply being that possibility. So, to represent itself as being concrete the world just needs to be concrete. Similarly, if a world is to represent the possibility of a talking donkey, it will do so by containing a talking donkey as a part.
For the abstractionist all possible worlds--- even the actual world ---are abstract. They represent possibilities in different ways. David Lewis lays out three different types of abstractionism (he terms the view "ersatzism" and the worlds "ersatz worlds"; that terminology has stuck in the literature, imo) based on how the worlds represent possibilities (See On The Plurality of Worlds, ch. 3).
- Linguistic Ersatzism: This is the version defended by Robert M. Adams (will have to dig for a citation later) and holds that possible worlds represent by saying a possibility is a certain way. One version of this view holds that possible worlds are maximal consistent sets of propositions, completely specifying some way the world might be. The actual world is represented by a maximal consistent set of propositions describing the way the world actually is.
- Pictorial Ersatzism: Possible worlds represent by isomorphism, like a picture or map. A map of the USA represents the USA in virtue of depicting 50 states in the right spatial arrangement, etc. This is how possible worlds represent, they're like pictures.
- "Magical" Ersatzism: Possible worlds represent by magic. This is what Lewis calls views, like the property view of Robert Stalnaker, that don't explain--- and, Lewis claims, leave mysterious ---how worlds represent.
The point here is that whereas a concretist can identify the actual world with this concrete thing we inhabit, an abstractionist will generally (always?) have an abstract surrogate for even the actual world. None of the abstractionist's worlds are (or could be) concrete, though many, if not all, represent possibilities involving concrete objects. Remember that not even "the actual world" is concrete for an abstractionist--- though it certainly represents a concrete possibility (ours!).
Your argument contains a false assumption: abstract worlds could not possibly be concrete, they just represent possibilities involving concrete individuals.