Like in that first PS4 Spider-Man game, there’s a bit of dialog spoken by JJ about Spider-Man being one of the first superheroes on the scene, and people took that personally (i.e. Vulture, Electro, and Doc Ock to an extent).
Similar with the Arkham games for Batman. Those are supposed to all take place before the Justice League or even Superman are around. You hear little throwaway lines of dialog in Arkham Knight about a “freak in Metropolis,” and SSKTJL takes place during his time with the JL. It’s supposed to be similar to his career trajectory in the DCAU, which started with Batman: TAS and ended with Justice League Unlimited/Batman Beyond.