It's even more blatantly clear in the remake, where blood stains the screen, and clearly is coming from her. Not a minute later, it's revealed that she's been shot and dies.
Then she's killed after twenty minutes in. Her death shattered him, and it took 20 years before he moved on from it. Once he calls Ellie this after she broke down after murdering David in self-defense, it showcases he nows sees Ellie as his surrogate daughter.
