I don't know too much about the Deus Ex world, but in fiction there is always the possibility that the timeline is different than the Earth history we are so familiar with. Perhaps the technological breakthroughs that occurred in the 90s for us happened in the early 1970s in Deus Ex, leaving a lot of space until the 2020s.
But how do you tie it in with the origional game? that's the problem..
Deus-Ex had a very different style to it, the whole world looked very much like it does today, just more run-down, and you could see more modern tech was retrofitted to old infrastructure, and i'd say that was it's defining feature, it made a belivable not-too distant future, one in which new tech was employed, ofcourse, but that didn't mean they had the resources to tear down all of New-York city and build a new future-cool city in its place, which probable woulden't happen in the real world either, and the new tech itself looked like something that could be the next step up from our current tech, it was advanced, but never so advanced that it seemed terribly Sci-Fi.
Infact Deus-Ex deliberately held back on the Sci-Fi, they could have given scientists HEV style suits, but they gave them labcoats, they could have added flying cars, but they had helicopters, they could have made advanced synththetic muscle style robotics, but robots where clunky and mechanical, they definately wanted to keep things relatable, something that we could imagine our current tech becomming in a few decades.
But this new Deus-Ex is very different, it's very cyberpunk-renisance, very.. Bladerunner meets The 5'th Element, the tech looks a 100 or more years ahead of Deus-Ex, but it's supposed to happen in Deus-Ex's past, the two do not look connected at all..