... Putting aside my other reply, I'd say lewdness isn't required, it's love. Saiko definitely lacks in love and care due to being unquestionably insane.
In the game, when she's not stabbing you, she shows admiration, just simply being happy staring at Akira, grinning like an idiot, and when she is hurting the player character, she's being sadistic. She loves 'playing'; torturing the character.
Is she a regular murderer? Nah, not really.
Is she a regular Yandere? Nah, not really.
But I guess, what even is a regular Yandere if they're meant to be irregular of mind?
Conclusion, she's just cray-cray and you gotta deal with it.