Depending if a game is motion capture or just voice acting, the game might not need the voice actor until very late into the game developement.
The voice actor for Morgana (Cassandra Lee Morris) just revealed that she voiced the English version of Persona 5 Strikers this summer and look how long that game has been out for the PS4 in Japan.
And voice acting a video game is not months of work. That is why you tend to have the video game nearly done, so you can get the voice actor to do all the voice work all at once.
So I would have been very surprised if the Voice Actor was already called in for Spider-man 2.