Well, if you actually listen in to the Killing Monsters music, the same theme as people have linked you to is used. The background music for the action is just that - background music created specifically for this trailer, which is why it flows with what's happening on screen, that's its purpose. But at 1:48, when the wolf head appears, is when the actual theme is played, which is, as I said, a more up-beat version of the original witcher theme.
For me, it fits the world perfectly and is easily recognisable. So no, I don't want it changed.
Yes, this theme definitely is a visit card of The Witcher series. Most of the inspired music include it in different ways.
Intro in Michal Cielecki's "A Short Tale" is one of my favorites.
https://soundcloud.com/michal-cielecki/a-short-tale
But on the first place for me is "Tales Of The Witcher" vokal version.