Well if we look at the Amano art:

http://www.gameforms.com/games/plays...1-amano-03.jpg

The horned figure seems to have a mirror showing some girl. From what I remember there was only one female in FF1 who even made a tiny impact on the game; the Princess of Corneria, who Garland kidnapped.
Of course it could be a Knight looking at her so he can go save her, but seeing as it's task #1 in the game it's impossible that a Knight job class could go save her. So my guess is Garland. Maybe fighting the dragon was to give him alittle more character or something, and make him seem more significant.