Fez (2012)

As the player, do you interact with a character or an avatar and how does this affect your involvement in the narrative?

Gomez is the main character introduced to the game, but h's a bit of both an avatar and a character. He is a character because he is an established citizen of his tiny town who already knows his neighbours, but he is also an avatar in that he is plain enough for the player to project their own characteristics onto him, even though we're given little. if any opportunity to do so, with most of the character 'interactions' being through Dot your 'guide'. The most emotion Gomez has to offer is an ecstatic 'happy' face when he accomplishes a goal, or plays with his fez/falls asleep on the floor in one of his long idle animations, showing off his childish personality.

Gomez suffers from a case of 'silent video game protagonist' and ergo, we cannot discern Gomez's thoughts on the possibility of his whole world and universe's imminent collapse. He isn't given the opportunity to express his own distress, confusion, or fear, or even any interest in starting an adventure. his emotions are instead left up to the player to project onto him and the player's motivations in the game narrative become his.

Gomez's status as 'character' from being an established character does not affect the game very much, as it is only a means to give Gomez a connection to Geezer who introduces him to the power of 3D game core mechanics. It's an underdeveloped bond between these two characters that stems from simply that the village, including Gomez are descended from the same people who were once gifted the view of 3D sight and that is the sole reason of connection, but Gomez is not aware of it yet. There is no further explanation as to how Geezer and Gomez know each other or why Geezer trusts Gomez with this power out of all the other villagers, but the brief backstory of a 'bond' simply creates an easier segway into kicking off the adventure, Gomez's identity as a character does not show much, nor does it impact the narrative of the game, since the village's identity is not very important to the overall narrative,  as if the Fez was simply a magical artifact rather than a lineage-specific item any character could have been tasked with saving the world, descended from mystical village or not if the lore was changed so that anyone who had the fez could see the 3rd dimension, Therefore it is clear that Gomez is more of an avatar in nature, than character.