I actually haven't had time to read the article yet. Posted then ran off to eat dinner. But time travel, at least to the future, doesn't require infinite mass. I can't imagine what they mean by that. Will read now and see. And, as I mentioned at the top, it happens everyday, all around us, to an almost imperceptible degree (only high accuracy atomic clocks can detect it).
Mass approaches infinity as an object approaches the speed of light. This is why an object (with mass) can never reach the speed of light.
Precisely at the speed of light the oblect's mass would be infinite (an impossibility of course).
Two other things happen as well. The object's length approaches zero, and a tick of the clock grows to infinity.
All of these things are realized from an outside stationary observer's point of view.