Ok, a few points that are wrong there:
1- His passive, Backstab, never worked with items. It actually only worked with his Q, Auto attacks, and E. Not even his boxes and clone explosion worked with it (although clone's autos did), let alone items. The only item it had a meaningful interaction with it was IE, as the crit damage would be applied to his AA's and consequentially increase the 50% bonus crit damage by it's 20%. Lich Bane, Gunblade, Protobelt, Smite, Ignite, Luden's, and any other items or summoners that dealt damage never received a bonus from Backstab. At the very least not in this last season. Might have been different in season 5, but I'm almost sure it wasn't.
2- His E has 5 base damage at level 1 and 3% missing health (which is increased with levels rather than ranks), as well as scalling with 75% of total AD. This means that, up until level 11 or so, in which it has about 2-3 ranks and the 8% missing health, the Shiv is basicly a weaker auto attack, specially since targets have a smaller health pool to be used with the % missing health. Unless Shaco is also packing ignite, he won't be getting that many early kills with this skill alone. With some quick maths, it should be dealing about 15-25 extra damage early game (depending on runes and masteries) to a target with 700 missing health. If you are missing 700 hp on the early game and is not recalling under your tier 2 turret, you're asking to die.
3- Ap Shaco still has some rather bad clears due to his lack of AoE. The boxes in the early game are not that much tankier and don't make such a huge difference. However there is no denying that the new jungle helps AP Shaco, both due to easier buffs and due to more gold and XP.
4-
he had a really easy time proccing those befor the assasins update, and many other melee-aps have a just as easy way proccing them without beeing an issue.
See, before the update he had only a 120% AP Scaling on his kit with his E backstab. After it, he was given a 72,5% on his Q Backstab and a 90% on his E, granting him 162,5% AP Scaling on his burst, making AP Shaco much stronger. He basicly gained a stronger Lich Bane on his Q after the rework. This makes a whole world of difference when you lack sustained damage and NEEDS to one-shot your target or die.
All in all, AP Shaco now does what AD Shaco was about, deleting a single target quickly, but faster. In exchange, his DPS is miserable.
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at the same time, resulting in an obnoxiously huge burst of damage.
he gets 567 AP. This translates to a 1643 damage burst happening instantly out of stealth on his Q alone. Without Thunderlords, Lich Bane, Runic Echoes, and Gunblade damaging passives/actives, he'd deal 527 damage on his Q.
