The article you posted is suffering from semantic leak. The words "layered" and "tiered" have many, subtly different meanings depending on who you're talking to. I, personally use a broad definition: a layer or tier says nothing about where the code is running.
The main benefit is that by having your state, interface and actions split up it becomes simple to change the way each of those are executed or handled. Data could be read directly from a database, with the actions running on a remote machine communicating with the client via RPC. Plus when separated it's generally easier to use codegen for each part targeting various platforms (ideal for implementing client-side validation!).
For LOB or data-driven applications (which I'm assuming is the standard use-case for Silverlight compare to JS/HTML) you would be advised to implement a service layer over your domain-entities. That gives you platform-level separation. Or at least it should, as that's kind of the whole point :)
With a service-layer in place, you have some kind of translation on the boundaries. For example you access your domain via a webservice, which serializes to XML, JSON, whatever, which is then reconstituted on the frontend.
These conversions should be totally automated and preferably nicely wrapped on the platforms supporting each layer.
Depending on your exact problem, you could even approach something such as Modal Driven Architecture. There you define an application as a model (usually UML), and then use that as input to your multiple, target-platform-specific compilers. This is particularly suitable to for CRUD systems: from one UML model you can generate a complete database, object model, winforms and web frontends. Though, to be honest, I'm not sure if there are many examples where the resulting interface can be described as "high quality". Oh, and from what I've seen the motivation for using such an architecture has been more to do with technical deficiencies of the modellers than any benefit over other methods. Though, as with everything, that's far from a rule. If your problem is easier to user-stand when it's modelled visually, and it's worth trading potential UI quality for it, then that's great.