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.

Not entirely seamless, but if you do a good job jointing the pieces and select boards that look very similar in color and grain, you can get close enough that most people won't notice them.

This tabletop is made of three different boards. No fancy joinery, they're just butt jointed with PVA glue.