I think it surely can count as a ballad in the original sense of the word-- it used to be that "ballad" just meant a song that tells a story.
But I agree that on the Ballad Collection they mean "ballad" as in "a sentimental love song", and Alive is much different from the other songs on that album.
Always thought it was interesting that they included Alive on that album rather than Voiceless Screaming... but Alive is a Yoshiki song and Voiceless Screaming is not, which I'd say is the answer right there.