The general point is not. Iceland and Easter Island were fully deforested way before the industrial age. Countless species went extinct in Britain and more examples abound.
Britain was a little bit industrialised even before the steam engine. There were windmills and water mills. Steam massively accelerated it, but industry did exist before.
If a windmill or a water mill is a sign of industrialisation, then large parts of the world were industrialised.
Commons in England were being enclosed in the Tudor age. It caused a great deal of social unrest, even rebellion. It had little to do with technology, and was mostly caused by population growth.
the speed at which depletion happened was probably not the same