The idea for presenting the skills and abilities is really a new, fresh and foremost *great* idea. Unfortunately, though, this thing is hardly usable.
For short ability-chains, you can easily catch those lines and arrows on one sight, but finding out what you need for stuff like Urgash's Call, Arcane Omniscience or Howl of Terror is practically impossible. You just can't track down all those lines, twisting, turning and crossing each other, going in totally different directions and distracting your clear eye.
I think this could be optimized - so there is still hope


Furthermore, I'd increase the size of the arrows and darken their color for better contrast.
I hope, you can make top-down tracing as easy as the way up from the bottom!