Is riven an assassin? or a fighter?

Riven is a Code Exploiter.

It is a class of champ that are allowed to exploit bugs until they are widespread enough to be called "features".

Last I checked, Riven is of the skirmisher subclass, sibling to the assassin subclass as they are both under the slayer class.

So I'm not surprised.

She is a subclass of Slayer called Skirmisher (previously referred to as Duelist). Assassins are the other subclass.