Technically, you're wrong & Aman is correct.
First person in writing looks like "I go through the door."
Second person "you go through the door."
Third person, "he goes through the door."
You can't call second-person first-person just because video game displays only come in first and third Person views.
Anyway, to your original point- write it however. Any viewpoint can be great or terrible, depending on the writer.
I don't think a story is any less immersive depending on its viewpoint.