Scything is relatively easy on the back compared to a lot of other traditional agricultural work. A scythe is designed to minimise leaning/bending over, and is driven from the hips and legs. It is important to have a snath (scythe handle) that is long enough - scything while stooped will put a lot of strain on the back. If you want to cut a wider swathe, you can lean over (to the sides and forwards), and this can strain the back, but (a) if you're doing this as part of your work, you know how far you can lean over to keep the strain on the back acceptably small, and (b) if you're doing this for a modern scything competition, you're not doing it for very long.

Bending over using a hand sickle is much harder on the back. Other tasks that require bending over like planting rice seedlings, harvesting root crops, some styles of hoeing, and many more, are also hard on the back. (Many traditional grain-grinding tools are also hard on the back. While not strictly farming tools, they were often used by farmers.)

Other tasks where the tool is long-handled enough to allow the user to stay fairly upright, like some styles of hoeing, and digging with various tools, are also harder on the back than scything because they typically (a) require more force, and (b) require more bending over.

In addition to what /u/wotan_weevil summed up perfectly, you need to remember that scything, like most agricultural work is usually done at a rather slow pace. The corn will not run away and there is no need to hurry (doing work fast instead of well is relatively new concept, hailing from Industrial Revolution).

It should be also noted, that mower has to take frequent breaks to maintain sharpness of the scythe with a whetstone. It is maybe not the rest per se, but it allows to straighten up and take a breath. This is especially true if one uses a scythe made of mild steel, common in continental Europe. Also, despite impressive size, scythes are pretty lightweight.

It also seems to me that the girl in a gif does it pretty inefficiently, as she sets her legs widely apart, forcing her to swing the scythe with arms and shoulders. An equally efficient and less taxing way to do so is an exact opposite - keeping one's legs straight and rotate hips, using upper body just for holding the scythe and controlling height of the cut. When done properly, mowing with a scythe can alleviate back pain caused by a work requiring slouching or bending for a prolonged time.