Virumor,
Choice isn't integral to a RPG, stats are.
As a tabletop gamer, you should know that the reverse of this is true. A character that is defined solely by their stats is no character at all: a true character is created by the choices you make for him/her.
This is why a good GM will always pay far more attention to the abilities of his/her players than the stats on their character sheets when planning out a session.
I can and have run tabletop sessions where not a single die was rolled nor stat consulted. Because role playing is about characterisation, not number crunching. Always.