What I don't understand is why stabbing a guy with a dagger should damage him more than stabbing him with, for instance, a shortsword. Maybe you get a bit more precision, but surely not enough to make stabbing perks exclusive to daggers !?
No, you don't get them exclusive to daggers. The thing is, when you sneak, a sneak-attack gets you different multipliers, depending on your weapon. In Oblivion, you got a 6X for blades, 3X for arrows. I'm assuming that that all stays the same, and they just added 10X for daggers.
Now, to balance the whole stealth archer thing, they should get rid of the sneak attack with arrows. Whether they notice you or not, your arrow is still going to go where you aim, so you shouldn't get a sneak attack bonus (especially since they made arrows deadlier anyway).
Blades are already more powerful than daggers, so a 10X for a dagger is very reasonable, and if you sneak up behind someone with a dagger and considerable skill, you should be able to kill them in one quick attack, thus justifying the 10X.