Many systems have mechanics that give the players as much ability to affect the outcome of a social situation as a fireball does to affect the outcome of a combat encounter. This is wholly in addition to, along side of, or outside of the player's ability to roleplay by having their character act as though they were a different person than they are or to suspend disbelief about an imaginary world or act out as an actor or voice actor a given character.
Indeed, many systems don't call them "encounters" at all. They call them "scenes" like you do in a movie, because every scene -- combat or otherwise -- is intended to move the story forward.
Many games have actual mechanics described and detailed in the book that give the players scene level control or even overall narrative control. Some systems are wholly collaborative storytelling and the game master doesn't prepare a storyline at all. It's up to the players to determine, drive, or alter the story, and they can do so directly from their character sheet as easily as in D&D a Rogue can pick a lock, a Wizard can cast a spell, or a Fighter can dispatch a goblin.
These are not generic resolution systems like 5e D&D's skills. They're deep mechanics with more narrow focus and more potent control. One recent example I can think of is from a Blades in the Dark video from Zee Bashew. In it, a PC playing a thief has to get past a guard. The player expends a resource, and says that the NPC recognized the PC as a former cellmate from a prison, and the NPC agrees to let the PC pass freely. The PC has now changed an NPC's backstory and contributed to the world and narrative.