"We Interstellar now?!" - BioWare
Really, this is all it amounts to. Just how Casey wanted ME3 to be Deux Ex: Human Revolution IN SPACE, the ME:A dev team wants it to be Interstellar: The Mass Effect Edition.
Wormhole travel doesn't cause time dilation because it doesn't involve near-light speed velocities. A wormhole is a shortcut through spacetime. The whole point of wormhole travel is to avoid time dilation.
While technically true, like I said earlier - the OP's basic concept is correct: Wormholes can allow for travel through time as well as space, and this is a viable solution in general relativity. It makes intuitive sense too, as spacetime is a unified construct and the wormhole is an extreme example of warped spacetime. The basic concept involves creating a wormhole, and then accelerating one end of it (there are various ways to theoretically achieve this) such that the destination end experiences the effects of time dilation relative to the departure end. Consequently, the traveler traverses both space and time.
So, a traveller that traverses the Milky Way wormhole in the 2180s could arrive in Andromeda in the 3180s, while experiencing only a tiny fraction of travel time. In this fashion, the game could take place "both far into the future and far away in space", but ALL of the tech would be 2180s tech, or slightly more advanced, and thus present a familiar setting.