My guess is that the 'darkness' is more atmosphere - I know nothing about chord progressions or anything like that (except knowing that both Alice In Chains' "Would?" and Carol of the Bells both use Phrygian mode, which explains why both of those are dark and depressing in tone), but said progressions can influence the way music is 'felt' by the listener, and it could also have to do with the choir-like background vocals, what sounds like a drum machine, and the vocoder effect.
The video having a lot of shadow in it probably doesn't help, either. I guess it's just somewhat ironic because "It's My Life" is generally regarded as one of the more 'empowering', I guess, anthemic songs from the past decade (being that it was released in 2000), rather than a downer. Really, it's almost like "Livin' On A Prayer"'s sequel, as they both are about enduring.