In a Gladiator Fight does a thumb down mean kill him?

The "thumbs down" was not a thumbs down, but a thumbs turned (to the side) which indicated that the victorious gladiator would cut the throat of the losing gladiator. If you want more information a good website is:

http://ancienthistory.about.com/od/games/a/thumbsup.htm

This is where I confirmed what I learned in a college history course.

In short, yes it meant to kill the man.