Not to mention that the Linux multimedia API is completely different from the Windows one. Indeed, while the codecs are the same, the interfaces exposed to programmers is completely different.
Adding to that, Linux has not one, but at least TWO APIs, depending on which desktop environment you're using. It'll be painful to maintain such a core feature across two platforms with three different code bases.
I'm not sure what J River's stance is on this, and I've not tried, but you may be able to run it using Wine since they have some DirectX emulation layers. You won't get bit-perfect audio like you can on Windows, but at least you get the library management stuff.
Jim/Matt/mods: if the suggestion's inappropriate, feel free to remove it, just let me know.