There’s a reason the automaton draws that particular scene instead of any other image from the movie. For one thing, that image of the moon, with a spaceship landing in its eye, is one of the most famous shots in all of cinema. It's a nod to the wonderful history of the silver screen and a tribute to one of moviemaking's great innovators—Georges Méliès.
Plus, it's a hint of what's to come. That movie, and the automaton, were some of Georges's greatest accomplishments. So when he's reunited with them, thanks to a little help from Rene Talbard and Hugo, he can finally accept his past and be proud of his history, failures and all.
And now that they've all seen the movie, Hugo and Isabelle can share in the significance of Georges's achievements, as they do at the ceremony at the end of the novel:
And then, the last film shown was A Trip to the Moon.
Hugo looked at Isabelle. Tears were running down her cheeks in two thin, glimmering lines. (2.11.24-25)
See? If it weren't for Georges Méliès's magical genius, Isabelle and Hugo might never have found each other, and this awesome new family might never have been made. We have the man in the moon to thank for that.