This scene gives us our very first backstory of Ellie our lead, showing us the only meaningful human relationship she has had in this post apocalyptic world (Riley) and how she lost this relationship. It also shows us the aftermath of when they got bit by the zombie, which in Ellie's case, is a very important plot point to note for the story. Riley is the only person Ellie has ever connected with, so losing her is a very important moment in the overall story because it demonstrates why Ellie has become the way she is.