Good examples for me would be IEYTD and the ESPER games. I felt immersed and entertained even though I couldn't freely exlore the environments. I think the main problem with this game that is people were simply expecting it to be a slightly different category than it turned out to be.
How can something be immersive if your not moving about in your environment and just teleporting everywhere? I wish devs would consider giving people both options.
I think any game where you are meant to traverse through locations they should include the option for free locomotion. If I see something in the distance I want to walk there, not suddenly appear there, the 'journey' is half the experience, like climbing up a mountain.
I expected, probably naively (or wrongly) that with Wilson's Heart being a narrative driven game where you explore a hospital, it would have full locomotion