Thinking about it some more, they must be using Z along with luminance, otherwise wouldn't their method blur any texture that had luminance variance within it, whether it was an edge or not? Then again, maybe that's why their game has that overall soft look to it.
Well, normally when you do some kind of morphological AA you are very conservative about what you consider an edge (the staircase patterns), so that shouldn't happen too often in textures, and when it does it's usually something you want to filter anyway. You can of course get sampling issues where lines that shouldn't be connected are connected and things like that (again with subpixel features).
Now, I'm not saying that screen-space AA techniques are a cure-all -- I've worked with them too much for that. There are a number of problems that have been lamented in the relevant literature since the 90s at least, and I'll try to summarize them here:
The one that's simple to see and has already been mentioned in this thread is whenever you have some feature that is sub-pixel size: you get exactly as much flickering as you would without any AA, since the edge detection doesn't have anything to work with.
This is a general problem with the method, but it doesn't decrease IQ below the previous state - it just doesn't improve it.
The second is harder to see (only in videos), but arguably a bigger inherent problem since it could decrease perceived image stability. What happens is that a slight (1 pixel) change can affect how a whole edge is interpreted. So what you get is a very different edge from one frame to the next, and maybe flickering back and forth between those states. (As opposed to only a single pixel flickering without any AA)
The third problem is not inherent to the technique, but only to the specific implementation used here. Since they use only luminance, they miss hue/saturation edges. (see my previous post) I think this is not a bad trade-off on current hardware, since I also had a rather difficult time finding those edges at native resolution. It's also a problem that could be solved easily at some additional cost by also looking for Hue/saturation edges.
Then there's a fourth problem with this particular version that I don't get at all: Them filtering the UI. This has some really ugly effects on stuff like circles and fonts and is completely unnecessary.
Anyway, the edge quality for sufficiently large feature sizes is still superb particularly considering the computational cost, if you can live with the minor drawbacks.