The Darkin (aka fallen Ascended) did in fact have animal appearances. In the origin story (the one with the amphitheater and betrayal), the Darkin's visuals are constantly described. "Fangs, scales, fur, etc.". That means that yes, before the betrayal, they had the animal-like appearances. When they were trapped inside their weapons, they lost their body altogether and the only way to gain another body was to steal it from a mortal that wields them. So over the course of time merging with other body forms, and a little bit of magic, the Darkin attempt to mirror their original image.
The Darkin don't look "shuriman" because they lost that appearance the moment they were trapped in a weapon. But keep in mind, one doesn't have to have been trapped in a weapon to be considered Darkin.
What Phieldworker mentioned below is incorrect. "Darkin" is simply a name mortals used to describe the Ascended that have fallen back into their original human-like state of minds, full of lust for power and destruction. They're just fallen angels, in a way. Shurima fell whilst they were fighting the void, and the void helped corrupt their minds in many ways (possibly hindering the "valiance", "pride", and "heroic" nature, maybe?). And when they hear the shit news that their lord died and home destroyed, that corruption in their minds influenced them to see it as "every man for himself". "I'm the strongest, I should lead." "I'll take what I want." etc.
There was no dark magic that twisted their appearance and made them blood thirsty.