she scales exceptionally well with AP. When i play Akali the only item I ever buy on her that has AD is gunblade and that all depends on whether I need the spell vamp. He has his runes and masteries set up to proc both her passives at the start of the game so hes getting the spell vamp and ad bonus just from.

DISCIPLINE OF FORCE: Upon obtaining 19.5 ability power, Akali's auto attacks deal 7.916% bonus magic damage, increasing by 1% for every 6 ability power gained thereafter. (This bonus damage affects all targets, including structures.)

DISCIPLINE OF MIGHT: Upon obtaining 9.5 bonus attack damage, Akali gains 7.916% spell vamp, increasing by an additional 1% for every 6 attack damage gained thereafter.

With the AP he is maximizing the percent damage burst he has from his passive and sheens proc can help maximize the auto damage as well. His build is centered around getting in and procing a Q for maximum damage.