Currently being trained to work as a German tax official, so I can really only offer the view from my own country for this, but here goes:
The "donations" that the streamer receives are part of the income he makes from his professional activities. He improved his behaviour, his presentation, his entertainment value in order to be able to receive these "donations."
Because of that they are considered business-income and NOT tax-free. He had the intention of receiving money for his streaming, which is the deciding factor behind it getting taxed.
It would be different if he were to do it as an actual hobby, without any intention of making money out of it. Those things are tax free here.