The backrest can certainly be modelled in SketchUp, either with native tools (a lot of work) or with the help of plugins. But it looks to me as if it came originally from other software, perhaps directly from the manufacturer's original files (Solidworks, Inventor or something like that).
If I was modelling this I would try to make a much simplified version. This model has, for instance, all the minuscule roundings that serve mainly to bloat file size and make SketchUp slower. Imagine what will happen if you model a large classroom and place, for example, 100 of these in it.