This image has the look of one taken with the HDR technique, yet it is a live performance therefore would be extremely hard to do, as the subject would be moving around. I used photoshop, Gimp and HDR techniques but don't know how to accomplish this kind of image. How do you think it is done?
As you say, it would be very hard to make a real HDR image of moving people, so that's most likely not how it's done.
It looks like it's just a regular image, but processed with a lot of contrast. Perhaps using curves to get the right contrast in the right part of the tone range. Bumping the constrast also makes the colors more vibrant, so you get this kind of look by also reducing the saturation.
A problem that you often face with that kind of processing is that the background suffers when you make the main subject look the way that you want it. It's very possible that the photographer split the main subject and the background in separate layers, and processed them differently.
It could be a combination of filters, saturation adjustment, etc. Or it could be a 'fake' HDR in which one raw file is taken, then virtual copies made in something like Lightroom. You pull back the exposure on one, increase the exposure on the other, then send all 3 pictures (with identical image but different exposures) to an app like Photomatix and it processes them as if they were three genuinely separate images... Then depending on the processing in that, the tone mapping applied, and subsequent LR edits after the resulting .tif gets reimported in, could all come up with something like that photo you linked to.
EDIT, upon second viewing of the photo, it may also be just a standard shot but with (amongst other things) the colour temperature dialled back quite a bit, this would explain why the lights and skin appear bluish, but the red of his suit still appears bold, if not quite as vibrant as it might normally do...
The image was almost certainly a single exposure processed with some local contrast enhancement, either with an HDR program or more likely the fill light function in Lightroom.
It's important to understand the difference between HDR images and tonemapping, which is the technique used to make HDR images viewable on low dynamic range displays.
See this question for details:
Could be normal processing with a lot of contrast, or could have used something like Topaz Adjust or LucisArts. While quite a different look, the image in this question - How to achieve the photo effect of Live Christmas Music... shows the high-constrast, HDR look that Adjust can produce.