I have not read much drama. However, I've still felt a lot from VN's.
999, my first VN (and my second favorite). I won't spoilers here (if I could, I could turn up a goddamn essay) but two of the endings just blew my mind and tore at my heart at the same time.
Virtue's Last Reward. Fear, happiness, sadness, mindfuck- I hate roller coasters IRL, but this was one hell of a ride. My favorite game of all time.
Steins; Gate's second half. Seriously...
Umineko- This VN probably made me feel all there was to feel, but it is too long for me to remember anything.
I love stories, and my hobbies are based on things that have stories: I love rock music for its meaningful lyrics, VN's my favorite video game genre nowadays because they have mastered storytelling, and I read fiction for the very same reason. They shape who I am and how I think, they give me unique memories and make me feel once-in-a-lifetime feelings.
VN's, for me, in their essence, are catalysts for profound feelings.