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But won't the electrical noise not to mention the other ports interfere with the audio?

That happens on most PC's. If anything, moving the audio away from the CPU, hard drive and main memory will reduce the amount of audio noise, since those components tend to throw off a lot of RF interference (so does the monitor & its fluorescent back light and control circuits).

If you want quiet, accurate, noise-free audio out of a PC, look for a PC that features optical digital outputs, and plug that signal into a power amp with an optical digital input. That's about the only way to get truly high-quality audio out of a PC.

Looking at an enlarged image of that system, it would appear they've put analog outputs on the main unit (destined to be a bit noisy I'd guess, as they are in most PCs and laptops) and the digital audio outputs on the power brick (looks like both optical and coaxial).