I don't think you're doing anything wrong, I think the dough is just more slack than you're used to. As @Jay noted, it can take some practice to work with a wet dough. But once you do, you'll be rewarded with a much more open crumb and a better final product. In my experience, I've found wetter dough and higher oven temps = better artisan bread (in general).
The recipe appears to assume the reader is familiar with the process, but does offer some hints. She talks about
scraping the dough out onto the work surface, then
The recipe isn't as wet as the ciabatta I'm making below, but the process will be similar, so I hope this is helpful. I start by putting a bed of flour down, then scraping the blob of wet dough out onto it.
Then comes the stretch-and-fold part, which is just as it sounds. Using a wet pastry scraper and/or wet hands, just get under one edge, lift and pull it away, then plop it back on top of the main dough blob. Then do the same with the other side. Cover with plastic wrap and walk away. There's no process of kneading like you're used to. This photo is after a few stretch-and-folds at 20-minute intervals (I think!), and you can see the dough has started to smooth out and become cohesive.
By the time you're ready to shape, the dough should be a lot more cohesive and easier to deal with. I folded mine into little slippers and put them on a couche to rise.
Add 500 degrees and a baking stone, and I'm rewarded with an open and gelatinized crumb, and a nice crisp crust.