To answer your questions: Noctie takes every move into account. Especially in short games or very one-sided games, a lot of the rating estimate will come from your opening play. If you play a bad opening, Noctie adapts and you will get an easier game, which may lead to simpler positions where you have less risk of making a mistake that would lower your rating. So what opening you play definitely has a big impact when trying to judge the rating from one game only.
If you create an account and log in, Noctie will accumulate information from several games to give a more balanced difficulty and more accurate rating estimate (and show how it changes over time).
Noctie's involvement isn't strictly required for the rating estimate although it creates good conditions for it by making the game balanced, not dominated by time trouble or trying to flag the opponent, etc.
Does noctie treat the opening any differently when factoring in ratings. I had two very different estimes - higher one (2100) was from an opening line i knew and lower one (1500) I left the opening more quickly but I don't think I played a much worse middle game. I'm closer to 1500.
Also curios if this could theoretically be applied to historical games as well or does it require noctie to be a participant. I'd love to see an analysis of how player strength has increased over time.