From what I can gather, "First-Person Adventure" is one of the styles of computer games. My understanding is that YOU play the game as though you're in it -- rather than moving around other characters that are not you (third-person adventure, perhaps).
Here's a description to back that up: In Titanic: Adventure Out of Time, you play an ex-secret agent, cast out of the agency for your failure to succeed in a mission on the Titanic more than 30 years ago. While you are in your apartment looking over the dregs of your life and the official expulsion from the agency, a bomb explodes nearby and somehow you are cast back in time, aboard that ill-fated vessel on which you disgraced yourself.
"First-person" is a familiar description in computer games, the most common being "first-person shooter". This distinguishes games where the player sees the action through the eyes of a protagonist (or sometimes from over their shoulder), controls their weapons and actions as if they were their own, etc. This is to give the effect of actually being a character in the game. Other games involve manipulating characters, often several, or entire armies, from a more omniscient point of view, often apparently from some point above them in the air.