So one thing I notice is I think you need to set a more accurate white balance. If you have WB set to Auto it's too blue. Either look at the ambient light source eg: diffuse light through a window or florescent lights and adjust the WB setting accordingly accordingly - Cloudy - Daylight - Tungsten etc... If that doesn't warm the image up correctly then read up on Custom or PreSet White Balance in the manual.
Beyond that (and sorry I am not a DSLR video expert by any means) I suspect you simply need better light.
Your example of a concert with black blacks is a good one as an aim but the big difference with your scene is that with a stage scene you have a very, very well lit subject so the camera is exposing for that and not surprisingly the black stage edges are black as night. You wouldn't get noise in that scenario because the camera(s) would be exposing for near daylight light levels on-stage: ie: low ISO, fast shutter speed etc..
In your clip the whole scene is uniformly dim. You didn't mention the settings for the clip (ISO, F, Shutter) but it looks like a noisy high ISO shot.
I just went quickly back and looked at some recent footage I shot in our local pub, the speakers are well lit (by pub standards!), the ISO I had set to 1600 and there is no noise visible at all. The blacks are clean and solid black. 1280x720. This is with a D5100, it can be done.
Lighting is a big deal with video and cinema as you know - if it were me I'd try and get a bit more creative with the lighting and use exposure compensation to under expose a bit for effect. Get a better white balance and lock the ISO at 1600 max as described above. Beyond that I don't know enough to troubleshoot further - but I agree, that clip is a lot noisier than you should be able to get.