I hear you about quibbling with details within a fantasy world, but the necessity of every work of this genre is to establish the parameters. The dead were the 'fast zombie' type and exhibited sentience, for example, as a contrast to the walkers in TWD. Arya was limited by the physics of Westeros so her leap had to be consistent with her physical ability, the jumping off point, etc. It's up to the writers to devise the scenario where she could do just that after having eluded a horde (of questionable size) of the dead and other WWs.
As an aside, I was mildly unsatisfied that they didn't tear around the library in berserker fashion rather than walk softly. If they knew an enemy was in the same room, I would think that they would just do the searching at top speed. If they didn't think there was an enemy, then what were they doing browsing the book collection? Likewise, as others have pointed out, the other WWs were wasted in this episode.
I didn't think, however, that the actual means of killing the NK was disappointing. Arya planned her tactics very well, knowing he would sense her attack. She played on his ego, allowing herself to seemingly be nullified by his heightened senses and quick reflexes. Plus, as others have said, Arya's back story made her action entirely plausible.
Now we just need to know what the heck Bran was doing all that time.