Why Diana, but not Riven
In the bloodmoon gametype...
Seriously looking at the champions, riven is almost more of an assassin based on riot's own definition and description.
:
3rd hit modifier : Auto modifier
Slow : Stun
Displacement : Displacement
Ranged/AoE Poke : Ranged/AoE Execute
Shield : Shield
825 Target Dash : 1105 untargeted dashing (obviously Diana can reset with her Q though)
Seriously, looking at these champions, on what makes them "assassins", Riven has an execute and escaping power over Diana. And i'm not even going to get into how Ekko and Yasuo made the list, while falling under the same classification as Riven.