No, the Civil War saga is not the fourth dimension in Spider-Man: Shattered Dimensions. It's just going to be an outfit that Spider-Man 2099 can wear and the only way you can get this costume is if you pre-order the game from Amazon. Pre-ordering from Amazon will also get you an art book filled with concept art, renders and more.
Nick just brought us the latest preview for Shattered Dimensions this past week and the game is looking pretty good. I'm still not sure if I'm okay that the game is now more of a linear experience compared to the past games, but I can deal with it so long as I can play as Spider-Man 2099.