How It Works
Stronger Mid-Game Powerspike
While AP and AD both have strong cheese power early game, AP's mid-game burst potential is much higher. Back in Patch 8.13 they also greatly reduced his E - Spinning Slash cooldown at rank 4 and 5. This means that at level 9 AP Tryndamere has quite a stronger powerspike than his AD counterpart.

Insane Damage Combination
When you combine AP Tryndamere with the Conqueror keystone rune, he deals a mix of physical, magic, and true damage all at the same time. His E will deal physical damage and his auto attacks will do a mix of all three once he gets Nashor's Tooth.

Amazing Cooldown Reduction
As an AD build, Tryndamere doesn't have access to heavy cooldown reduction the way his AP form has. This build easily gets to 40% (or 45% if you go with the inspiration mastery). This allows him to continuously spam his spells and out-trade nearly everyone in the game in short bursts.

Weaker Sustained Damage
Compared to his AD counterpart, this version of Tryndamere is lacking in lifesteal. As a result, continuously battling doesn't favor him. Although he will likely heal back to full after using his Q post-ultimate, this version of Tryndamere needs to make a quick exit if things turn sour, fury or no fury.

Slower Waveclear
AD Tryndamere can annihilate waves almost instantaneously. AP Tryndamere can do the same, but would need to rely on his valuable E cooldown to do so. If he chooses to save it in case he needs it, then it results in a much slower waveclear.

No Stormrazor Usage
As a single item right now, Stormrazor is incredibly strong. While you could potentially fit it in somewhere in the build, it would certainly be sub-optimal to do so.

Conclusions
AP Tryndamere is good right now, but then again, so is AD Tryndamere. His surprising viability as an AP champion comes largely at the hands of the reduced cooldown from his E buff. I don't think he's overall a broken champion right now, but certainly strong.