And what about the giant itself ? He has LOS to itself and is within 2 spaces . . . ?
Well, Sweep says that you perform an attack that affects all figures within range.
The "range" for a Melee attack is "an adjacent space." The space occupied by the giant is certainly within LoS, but it is not adjacent to itself.
Giants also have Reach, which "allows Melee attacks to target figures up to 2 spaces away." This could be interpreted as meaning "range within 2 spaces," which would include the Giant itself within the Sweep radius. Or it could be interpreted as a shorthand for "adjacent and 1 space beyond adjacent," which would continue to exclude the Giant in the center of the whirlwind. IMHO, the latter would be more consistent with the basic rules for Melee attacks, but I admit it's an ambiguity.
We should also consider exactly where this "2 spaces away" limit is being measured from. We don't pick a specific space within the Giant's footprint to measure from, as we would for a ranged or magic attack. That would leave the sweep radius lop-sided, rather the centered on the Giant figure. Instead, we measure two spaces out from all sides, putting the Giant in the center. In my opinion, that adds support for the latter Reach interpretation as well. We're taking all spaces adjacent to the Giant (which excludes the Giant's spaces themselves) and all spaces 1 beyond those as the AoE for the Sweep.
You can play that the Giant sweeps himself if you like. IMHO, whether or not the rules support that idea hinges upon how you interpret the rules for Melee attack "range" as discussed above. Zaltyre has already sent in the question, so we can hear what FFG has to say about it, officially. However, I already know which interpretation I support, official or not. =P