When I was younger (and had way less to worry about, I think), I had a much easier time investing myself into a character and living through them in a game world. Game's that allowed you to create your own character, define your past, and gave you tons of dialogue options were amazing (Infinity Engine RPGs primarily). Escapism at it's purest.
Nowadays though, I prefer pre-defined characters with well written stories that allow me to go along for the ride. Decision or playstyles that allow me to define certain characteristics are great, but I enjoy the idea of playing along with a character I don't know everything about. This allows writers, good ones at any rate, to surprise me by taking away control at crucial times (The Last of Us, The Witcher 3, SOMA).
Both are still escapism for me - allowing me to role-play myself in another world or to live vicariously through another character. The escapism I get from an hour or two of videogames every day is vital for me to function normally in the real world.