They sound normal to me. Geoff Tate his his distinct sound in his voice, Halford sounds like Halford, Dio sounds great, and so on. Their voices were similar because that's how 80's heavy metal singers sang.
EDIT: Interestingly, I listened again, and DuBrow does sound a lot like Dio in the first part!
I need to listen to Quiet Riot a bit more. Metal-Archives has all the lead singers listed, so here you all go. Overall, they have distinct voices, but Dio and DuBrow DO sound similar in the song.
Dio (guess
)
Dave Meniketti (Y&T)
Halford (Judas Priest)
DuBrow (Quiet Riot)
Eric Bloom (Blue Oyster Cult)
Paul Shortino (Quiet Riot and Rough Cutt)
Geoff Tate (Queensryche)
Don Dokken (guess
)
By the way, the song came out in 1986, so Somewhere In Time era Maiden is correct.