The way I look at, Fenix was focusing on getting the fastest possible mid game spike out of Corki, because of his abilities, the hybrid scaling, and his bonus true damage passive for %ad passive, Triforce is what gives him the biggest damage output for having one item.
As far as building into Luden's Echo and then Liandry's afterwards, Fenix was clearly trying to revive AP corki from season 3 (I think, don't crucify me reddit pls) worlds, where you would just spam bombs at people and have them die at a distance so your team could clean up afterwards. Since his ult is pretty low damage (except when he has a big one) and is mostly just about getting sheen procs ready, buying Luden's and Liandry's adds 2 extra damage effects to each of his rockets, massively increasing the average damage they inflict.
The %hp burn from Liandry's and the extra AOE/AP scaling from Luden's means he gets more bang for his buck in terms of AP, and is basically like adding extra AP ratios to his Q and his R.
This build allows Fenix to get the mid game tower pushing spike that a team gets from having 2 adcs and at least one triforce, but allows him to transition meaningfully into the later parts of the game where he's not going to want to look for an outright 5v5, because a normal mid + 1 adc will outscale 2 adc comps on virtue of there not being enough peel in a 5 man team for 2 adc players.
The build also brings a surprise factor because teams are going to see a double AD comp and spec heavy into buying Armor and HP, because even though Corki does put out a lot more magic damage than other ADCs, he is still mostly focused on dealing physical damage. Swapping into an AP Corki build after the enemy has committed to playing against a double AP comp, especially since he gets an extra 30 magic pen from Liandry's / Sorc shoes means that his abilities are going to be dealing significantly more damage than CLG was prepared to deal with
The build was clearly planned as you see he took hybrid pen marks, and magic pen glyphs in his rune page. Since the enemy cannot see these in a tournament setting (no op.gg for you, Link) it allowed him to reach mid game AP Corki, while still bringing something to the mid game.
TL;DR: Triforce gives Corki his midgame spike for tower pushing, and allows his team to make early plays without giving too much information awayy. Planning to swap into an AP build mid game after committing to one hybrid item requires that Fenix build Liandry's and Luden's because they greatly increase the efficiency of his bombs before he has end game AP stats. This build path not only grants a mid game surprise factor when he starts to transition into AP, but it also allows him to circumvent the weak early game of AP Corki by forgoing early poke potential of a Morello's or Athene's in favor of lane bullying and tower pushing potential.
Again this is just off of reading the history for the match, his set up, looking into the picks from both teams and speculating, but I can't come up with another reason why you would build this way if your goal wasn't avoiding AP Corki's bad early game, and surprising the enemy. Is this viable for solo queue? If you can pull it off and the enemy isn't watching op.gg/loking/lolnexus/elophant/etc. where they can check your setup and predict this. Is it a viable option for tournament play / LAN or any setting where checking setups is illegal? Maybe, but it depends on what your team's goals are for the game.