As BobM said, look no further than almost the entire genre, and most of its subgenres, of prog.
Most of these will sound epic in a different way than the Kitaro piece. To me, the Kitaro sample in the OP sounds a bit forced in the way it achieves its epic qualities.
The prog version of 'epic', comes from a basis of extremely high levels of musicianship, musical complexity, concept, composition. To me, the epic qualities from most of the following, have a more natural, organic feel in their epic-ness.
I used to be a Kitaro fan, but the way.
The classic era (70's):
Yes - Close to the Edge
Yes -Awaken
Genesis - Super's Ready
Genesis - The Musical Box
PFM - Storia di un Minuto
PFM - L'isola di niente
ELP - Tarkus
ELP - Karn Evil 9: 3rd Impression
King Crimson - Larks' Tongues in Aspic
More recent examples:
Anglagard - Hybris
Flower Kings - Stardust We Are
IQ - The Narrow Margin
IQ - Harvest of Souls
Hostsonaten - Winter Through
So many more bands and songs I could list.