>>Wouldn't that be more linked to reinforced wing structure?
Yes, you are increasing the wing bending moment with the extra mass at the tips
>>Are they really boosting the wingspan that much?
if the winglets are mostly vertical, then no. But neither were those on a lot of the early airliners... and yet they worked. Don't quote me on that because i'm not an aerodynamicist, but the general point of a winglet is to displace the tip vortex to a more favorable position, which often is (but does not have to be) outboard. The winglet, regardless of dihedral, is also designed with a forward component of lift.