Thank you for the (good) news: somehow Media Center runs in WINE under Linux.
I am stuck with soundcard configuration under Linux. My PC has an integrated soundcard on the motherboard and an additional Terratec EWX 24/96. I succeeded in hearing sound using the KDE control center, but no player could make any sound. So I paused my attempts. I am just at the beginning of my Linux experience. I think that configuring such a complex piece of software like Media Center to run under WINE is a little too far for a beginner (although stimulating).
I am so frustrated by Windows as an operating system that I am looking for a better alternative. Unfortunately it's not the operating system itself, but the applications that keep me stuck to Windows. There is no such a player as Media Center under Linux. Also, the few other open-source applications I have tried do not stand up to their Windows counterparts (but this is just a first impression, I might be wrong).
Clearly I would prefer a native Linux version of Media Center, but I understand there are so many OS-specific issues in the current version of Media Center, from playback engines to external device support, that a full rewrite of the software would be extremely expensive, and J River might consider it not worth the effort, as there are not enough Linux users out there on the market. That's business.