You can't install MC on the Dune, it needs to run on a separate PC (unless you can hack the Linux pre-installed on the Dune and somehow make MC run there).
If you want to use the Dune UI to list/browse the available content on an MC Server, then it should work fine as their specs say it supports a DLNA source (that would be MC).
If you want to use MC to browse the collection, hit Play, and see it played via the Dune, then you need to email them and ask if the Dune can act as a "DLNA Media Renderer" (ie, target device for MC to control).
The Dune supports a sort of HDMI-passthrough, so technically you should be able to connect both the MC server PC and a TV to the Dune's HDMI ports, to see the MC GUI on the TV. But then to start playback using the Dune as renderer... it would be strange and you would likely need to use the Remote to switch the video source after hitting play.