Antimatter moves mass not space. Its a no-go because of all of the issues--time dilation? You need to move space, but we still haven't found a way to fully create negative energy.
Time dilation is not necessarily a problem, it can even be a boon - depending on exactly what you want to obtain. In particular, time dilation means that you can have a crew that actually lives for the duration of a journey that takes hundreds or even thousands of years from our point of view (e.g. in an accelerated space-ship).
I believe they’re saying that antimatter functions, essentially, as a normal fuel (although an amazingly dense one, far surpassing the energy density of anything else we’ve ever used as a fuel). But it, ultimately, has all the drawbacks that are inherent to “normal” fuels.
But there have been proposals for other ways of traveling through space, that involve manipulating space itself, so the distance between point A and point B are smaller. Think of wormholes, or similar. One such proposal is the Alcubierre drive, which warps space around it to cause the total distance traveled to get from point A to point B to be much smaller.
But such exotic drives require exotic forms of matter that we have no evidence of