The Yahoo group Cybalist have the article as a PDF (it's only about four pages) in their members-only section. I've now read it and am blinded with statistical science: I have no idea what any of their fancy new tests mean. (I know what "bayesian" means, vaguely.)

But the basic point is they're not claiming to do anything other than glottochronology: they're just applying new statistically subtle tests to overcome the traditional objections that made glottochronology worthless. These were things like evolution happening at different rates on different branches; and borrowing between related branches fuzzying up the tree structure.

They tried all sorts of assumptions, and then tried varying them to see what effect they had. Words identifiable or questionable as borrowings would be included in some runs, excluded in others, or just marked as doubtful.

After huge numbers of comparative runs like this they found the tree was mostly pretty stable. The main difference was in the age of the base, down near where Hittite split off from the rest.

For what it's worth, here are the branching dates they came up with on their best tree:

Celtic into P and Q: 2900 years ago
Latin into Sardinian and the rest: 1700
Germanic into North and West: 1750

They then group Germanic with Italic, splitting 5500 BP, and that close to Celtic, splitting 6100 BP.

Slavonic into South and North: 1300
Balto-Slavic into Baltic and Slavonic: 5500

Sanskrit into Kashmiri and the other Prakrits: 2900
Iranian: 2500
Indo-Iranian into Indic and Iranian: 4600

Albanian dialects: 600
They group Albanian closest to Indo-Iranian, but still very distant (no date given), then group Balto-Slavic with Celto-Italo-Germanic 6500 and all the above 6900. This is a big fanning out in a short term, so they suggest this is consistent with the Kurgan theory: it is this division that was the Kurgan one. The only branches that appear older than that are Greek and Armenian, which they group together, splitting from the others at 7300 BP.

Earlier than this, Tocharian at 7900. Finally, Hittite unites with the rest of the tree at 8700. These dates are the most variable.

Well, I hope that makes some sense. This is just my lay interpretation! Don't judge their statistics on my poor reports.