I would have to agree that his eyebrows are very reminiscent of Alexei Nikolaevich's. The rest of his face is not quite as sweet, but a bit of toughness would have been beneficial in casting the role.
The role of Alexei would prove difficult to cast: one would need a boy of a certain age -- but also a sensitivity and depth of range beyond his years. Someone perfect for the role of a literal iconic youth in their prime would not be perfect for the role for long, and the role could launch the career of someone people don't know yet. Look at Christian Bale: whose first role, I believe, was a portrayal of the Tsarevich.