It's only "luck" if you actually know all the words - most people do passively, but can they find the right one actively? That's part of the 'skill'. The other part is constructing a mental graph that allows you to find your way to the correct word within 6 steps, regardless of the word. An interesting question is whether there is actually any luck involved and how much. i.e. What is the optimal graph reducing the luck factor to a minimum, and is there a perfect one, if you know all words in the game?

People who say "it's just luck" either don't know, or don't care - but it's neither a correct, nor a clever position.