This film takes place in the My Little Pony universe, before G1.The unicorns in this eventually evolved into many different colors and forms, thus becoming G1 ponies. Then, as the ponies developed technology, they lost their immortality in favor of human emotions. Humans went extinct, and G2 came, then G3, then G3.5, then finally the generation we know and love.
Haggard used to be a unicorn.That is why he is only happy at the sight of them, but he doesn't know why - he forgot about the time along ago.
Haggard is descended from the unicorn Nikos turned into a humanI know; Schmendrick said that unicorn didn't have any children. But, if he were mistaken about that, then Haggard being descended from a unicorn and a princess links in to his royalty, his dissatisfaction with life, and his love of unicorns.
Mabruk taught King Haggard to summon the Red Bull.Haggard seems more of a warrior than a magician, so perhaps the wizard Mabruk taught him to summon the Red Bull, or summoned it himself and bound it magically to Haggard. Mabruk was the cause of all the problems in the story, and gets away with it at the end, because after all, "Nothing ever ends", and there's always another quest to complete or villain to defeat.