Power metal and symphonic metal, as others mentioned, are among my favorite genres, and I found them through TSFH. Nearly everything written by TSFH, or its composer, Thomas Bergersen, will give you similar feelings. Audiomachine, City of the Fallen, Immediate Music, Epic Score, X-Ray Dog, and any other trailer music group all specialize in creating intense songs like the one you linked. Their songs cover a gamut of emotions, but the average song in this genre is pretty darn powerful.
Tastes differ even within this particular genre, but if you're looking for powerful songs, I've got a few you might like.
Two Steps From Hell - Release Me [https://www.youtube.com/watch?v=8D26vYP1Nxc]
Audiomachine - Wars of Faith [https://www.youtube.com/watch?v=3GjNX7jcLK0]
Two Steps From Hell - Star Sky [https://www.youtube.com/watch?v=pICAha0nsb0]
Future World Music - Dream Chasers [https://www.youtube.com/watch?v=ysusZfArPoI]
Two Steps From Hell - Never Back Down [https://www.youtube.com/watch?v=uZTkg8GGEOo]
Immediate Music - Preliator [https://www.youtube.com/watch?v=Yiapc462rEs]
City of the Fallen - Seraphim [https://www.youtube.com/watch?v=UPFun_DQgGY]
If you want powerful music with more defined female vocals, Nightwish, Within Temptation, and some songs by Globus might be up your alley.
Nightwish - Ghost Love Score [https://www.youtube.com/watch?v=uN3yqMr3ffY]
Within Temptation - Our Solemn Hour [https://www.youtube.com/watch?v=p4h1wciz45o]
Globus - The Promise [https://www.youtube.com/watch?v=DyREJ9PpD7M] (Personal favorite.)