It's obvious that it was a troll build.
They were using almost the exact same logic behind the infamous "Dunkmaster Yi" build where after finishing the AS jungle item (used to be Wriggle's Lantern) and a Boots of Mobility, the player would continue to stack Zeals which would them all build into Phantom Dancers. The unique passive does not stack, yeah, but the rest of the stats still do (the purpose of that Yi build is to stack AS, MS, and Crit, which all 3 Zeal and PD provide, in this case of Ahri's build, it's to stack both CDR, AP, and Mana from Luden's; while utilising the item unique passive that's beneficial to the champs, Phantom Dancer's passive is ideal for Yi, Luden's passive is ideal for Ahri), albeit typically with varying results of inefficiency but not outright unviable, hence a troll build.
.....
This Ahri based on other descriptions, isn't really a troll player themselves it would seem, just someone curious enough to try a troll build while trying to make it work.
That reminds me of the couple days earlier where I was trying AD Ryze because I wanted to run into fight to root someone and AA them to death. The builds didn't work out that well, though.