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Not enough has been provided in this article. What does "different" mean (in percentages or whatever)?
It is perhaps not surprising that those in distinct regional groups are "more different from each other than from the English group". Surely, the "English" group mingled with all of them, while they didn't mingle with each other so much? More importantly, do the apparent genetic differences between "celtic" groups indicate that these Celts were a cultural, rather than ethnic group? Maybe, but let's not forget that these same celts have a history stretching back to thousands of years before the invasion of Angles, Saxons, Jutes, Vikings and Normans. This is possibly enough time for regional genetic groups to form from the common root.
Maps of particular genetic markers would be much more useful in this respect and they should also include other significant areas at least (lands populated by continental celts and the invaders' previous homelands) as these are just as important in the story. If possible, these markers should be also traced back in time (as was done for the "Out of Africa" theory). Finally, some historical data would also be useful - remains of men from bogs, bones and such.
As it is, it looks like interesting, but it is only scratching the surface and far from conclusive. 

I think that there is at least a theory that 'celtic' was a cultural thing rather than a genetic thing

Jim

Just so long as its not a football thing...