It was playing audio from a sound card via S/PDIF to an S/PDIF DAC when I recorded that video.
I've now done a lot more testing, and it doesn't seem to matter what devices are used, or what is being played - whether it's audio via the WDM Driver or playback of a FLAC audio file.
I've tried combinations of Media Center and the game outputting via: S/PDIF, HDMI, DisplayPort, USB, and Analog audio. Via ASIO (where available), WASAPI, and DirectSound. With both playing to the same device, or different devices.
I have disabled all DSP in Media Center, disabled the spectrum display, tried all memory playback options etc.
I've minimized the window or started Media Server and closed the window entirely because I thought maybe it was the UI updating which was causing this, but it still occurs.
I've adjusted process priorities and affinities to ensure that neither were running on the same CPU cores (though CPU usage remained low regardless).
Even when Media Center is playing to the "Null" device it causes this stuttering to occur in games.
The only thing which does not seem to cause stuttering is streaming to an iOS device via JRemote - whether transcoding is enabled or disabled. Any form of local playback seems to cause stuttering.
It doesn't seem related to DPC Latency, as that did not appear to change with playback.