If there's multiple pieces, there will be seams, although they may not be visible in a video. This is one of the reasons people 'fake' bends: build up the structural wood from multiple pieces, which gets good strength while minimizing material usage, then cover the bent surface with a thin (ie, flexible & inexpensive) veneer, and trim that the to final shape.

Most of the methods mushroommunk described are good for curving wood along its long axis, making the visible/usable surface of the wood curved.

If you mean the desk top is curved, like a C-shape around the user, then they've probably just cut the curve into a big sheet or two of engineered lumber (eg. plywood), and covered that with veneer.