I finally listened to the song you posted. It wasn't bad, but it's not really my style. I think what you're hearing with the singer (at least part of what you're hearing. He does have a tendency to skip notes in live performances, but usually not on their records) is actually a restrained scream. I doubt you would enjoy this song, but it does demonstrate what I'm talking about.
If you listen to it, you can very clearly hear what seems wrong about his voice: he's in a metal band that interjects screaming into their ballads.