Most physicians wouldn't characterize catheter ablation as 'surgery', nor does the source NEJM article use that term, preferring 'ablation'. It's an interventional procedure done by a cardiologist via a catheter in the femoral or radial artery.

The properly-called "surgical" treatment for a-fib is Cox's MAZE procedure, which has undergone several modifications over the years and is sometimes called pulmonary vein isolation. It involves opening the chest and making a series of precise cuts in the back wall of the left atrium, then sewing it back up. It's usually - I dare say almost always - performed only when the surgeon is already in the chest for some other reason, such as surgical correction of mitral valve stenosis.