Is this like the old PS2 release of the game?

[Toxicwire†]

If not, is there a remaster of said game?

[Stormspark]

If you're referring to the game made by Treyarch, then no this has absolutely nothing to do with it. That was based on the Spider-man 2 movie. This game takes place its own universe and is completely different in both gameplay and story. No relation to any movie. This is a sequel to the first Marvel's Spider-man (on PS4, PS5, and PC) and you play as both Peter and Miles.

https://marvel.fandom.com/wiki/Earth-1048

There is no remaster of the Treyarch game I'm aware of. The best version of that is on the Gamecube.