The power of choice is very important in a game. If the player does not have much choice, then he will feel less powerful, which will naturally make him feel less immersed in the game. The less choices a player has, the less they will feel like they are playing the game but rather that the game is playing them.
Another criteria that is important is the linear vs branching narratives in games. Linear narratives follow the story line fairly straightforward and has one final ending. On the other hand, branching narratives have many paths the player can take that leads to different endings. Branching narratives give you much more choice within the game.
In Undertale, the player had the choice to kill or not to kill. As you moved your character around in the game, you would occasionally run into some monsters that you either could talk to and leave without anyone getting harmed or kill it and continue on your journey. You also had freedom of choice to walk anywhere you wanted and interact with anything you wanted. The player was in control the whole time, and there wasn’t really a narrative to guide you along. However, the more monsters you killed, the worse of an ending you would get. If you ended up letting all the monsters live, then you get the “best” ending. Therefore, the player has the freedom to make their own choices, but his choices led to different endings, which made Undertale a branching narrative.
On the other hand, The Last of Us has more of a linear narrative than a branching one. Although you do have control over what the character does, everyone who plays the game has the same experience since it is always the same narrative. There are no multiple endings that you can achieve by doing something differently, unlike Undertale. Everyone gets the same ending. However, the narrative for The Last of Us is much stronger than Undertale since the developers did not have to spend time and effort into creating several endings.