How do Software Defined Radios have such big bandwidth?
can scan it's whole frequency range (1MHz to 6GHz) in the same time.
How does that happen?

Not at all.
The HackRF (and other SDRs) can just be tuned to arbitrary frequencies, giving you arbitrary coverage (in chunks of sample rate bandwidth at once), but not simultaneous coverage. I'm not quite sure where Mossmann claims that it would, so I think this might be a misunderstanding :)