>The game took place in 2013 then it jumps 20 years in the future.

The game was released in 2013, yeah? There's nothing special about that year otherwise. So the outbreak started in present day, and the main story takes place in an alternate future.

With the show, they decided to set the main story in an alternate present. So they just subtracted 20 years from 2023.

Had they set the outbreak in 2023, then it might invite unintended logic questions related to the world's prior pandemic experience (Covid). Best to avoid of all of that and do the opposite of what the game did.