Although we might contend that all theater is in its way "immersive" some productions are especially designed to immerse the viewer in the experience.
Some of these include the very entertaining The Light Years (The Debate Society/Playwrights Horizons), the upcoming marathon Mourning Becomes Elektra (Target Margin Theater), theater activist Tom Block's play, Sub-Basement (Athena Theatre Company.) This is not all new, of course. In 2012, Roundabout also staged an immersive piece which we fondly remember, The Mystery of Edwin Drood. https://tandbontheaisle.wordpress.com/2017/03/14/surrounded/