Rule based mediums are not that great for telling a (linear) story or eliciting specific feelings due to the nature of rules. To achieve these goals it is best to be in total control of your work. Non-interactive media is author based so why wouldn’t some interactive mediums be author based too?
This is were things get tricky. Interactive fiction is a huge topic with many possibilities. For start you can take any non-interactive form of fiction and turn it into an interactive medium, for instance, interactive short story (made one of those in the past). This works for novels, movies, poems, the whole lot.
On the other hand interactive storytelling is bigger than that. You can tell stories in ways that are simply not possible with non-interactive media. You can create stories on the fly based on what the player does or procedurally generate them based on randomness.
For these reasons I will not try to list any interactive storytelling mediums. I will leave that to those who are more invested in this field.
Sometimes all you want to do is to elicit certain feelings and thoughts from the user with little to no storytelling, decision making or even interactivity! Looking around might be enough. In these cases you might want to consider Digital experiences.
Digital experience is exactly what it says on the tin. An experience in a digital form. Virtual reality is a great place for these. Another real life example is so called walking simulators. You play those to explore a space and feel like being in a weird, new place.
I will again abstain from an overly specific definition due to the vast possibilities of this medium. Other people will have to fight this battle too, once there are more examples to look at.