5B light years across–the largest feature in the universe

If it's significant then it is significant within a specific model and elements of said model should be able to be specified with logical precision - otherwise the said model is kinda pointless.

Clearly what they are seeing is a large scale anisotropy - so what's the treshold for an anisotropy to be considered to be 'a single structure' and how is it measured?

Think of it in terms of the Second Law of thermodynamics. Local increases in order (decreases in entropy), such as there formation of stars or the emergence and spread of life, apparently violate the law, but in fact do not when you look at a greater scope. Order is decreases at "the largest scales".

So by "feature" and "structure" he means a local violation of this principle of uniformity. Apparently this arrangement of GRB's cannot be random non-uniformity, thus implying it is some kind of structure. For example if you flip a coin a million times you will get some clumsiness, periods with far more heads or far more tails. But if clumpy periods exceed a certain size, you would start to suspect that the coin is biased or rigged. It would be violating your expectations given truly random coin tosses.

Or as skwosh said in another comment, "It's considered a feature I think not just because it's a ring but because it's an area of higher than expected density of Gamma Ray Bursts (GRBs)."

Heat death. If the universe grows infinitely we'll eventually run out of stars - but I'd worry far more about how we're treating Earth than such things.

I'd be interested to hear how they get this 1 in 20,000 figure.