The data (model + coefficients together with source citations) of the Lean ICT study are available (see below).
HD Video streaming consuming between 250 W and 1 kW power equivalent is plausible compared to a study from 2012 finding 780 W.
The Stiftung Warentest formulation cited by OP is IMHO misleading:
it does not mention the crucial fact that ...
The original research that produced this was done in a collaboration between the University of Glasgow and the University of Oslo, and UoG details it here. While the Glasgow part is available here, the part we are interested in is available here, but is $30.
From the summary, it looks like the comparison is between the cost to produce the plastic used in ...