This isn't correct: the entropy (and energy) of the gas cloud goes decreases as it collapses, but the entropy of its surroundings increases faster as it radiates.
Here's the relevant quote from wikipedia [1]
Recent work has cast some doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly, moving the universe further from the heat death with time, not closer. This results in an "entropy gap" pushing the system further away from the posited heat death equilibrium. Other complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult.
The video actually directly addresses the gas cloud question, saying basically that a gas cloud is actually a highly improbable distribution of matter, whereas the eventual planetary system is much more probable. The claim being, that trend towards expected state is entropy increasing.
Thermodynamics is not magic. In the same way that we can predict the evolution of climate without knowing where every single cloud will be, we can make statements about the evolution of large systems even though our knowledge of their state is imperfect. Again, nothing unscientific about it.