It's a brand new feature in MC for windows, but there's nothing comparable in MC for Linux right now. I can't speculate on when (if ever) it will be available in Linux; it's a fairly tall order.
On the windows platform some of the underlying architecture had been in place for a year or two: for example JRiver Media Center 18 and 19 both had some software loopback options (ASIO and WASAPI) that sort of laid the groundwork for the WDM driver. Nothing like that currently exists in MC Linux, and Linux uses a completely different audio stack than windows so they'd be starting from scratch to some extent. I haven't tried using that feature of Windows MC in wine emulation, but my guess is it would not work well.
The bottom line is that there isn't a good solution for this issue in the near-term on the linux side.