Presumably, Kontsevich is referencing the fact that Deligne used a "trick" to prove the Weil conjectures. Kontsevich is presumably talking about the Grothendieck standard conjectures on algebraic cycles, which would allow us to "realize the dream of motives".
I see no way to "moralize" Deligne's proof, because as I said, it relies on a "trick" which circumvents the hard parts of the standard conjectures.