The gameplay is just different enough from the original game (example in spoilers below) to make reading the instructions necessary, but I think this can be done during unboxing with the other players. If you would prefer to read the instructions ahead of time but still open the box together, they're posted online at Avalon Hill's website: https://media.wizards.com/2018/downloads/rules/BLY-Rulebook.pdf
As noted by @bwarner "The beginning of the rules also contains a "here's what is different from other Betrayal games" page. If you learn those things, and you've played Betrayal before, you will likely be good." This is page 3 of the rulebook linked above.
For the most part the Legacy deck will guide you through what's special about each chapter. Please note though that the rulebook itself will change during the course of the game, and should be reviewed during each session to re-familiarize yourselves with what's changed.
Gameplay spoilers (not anything plot related):
Events / Item cards, similar to tiles, can now only be drawn in certain zones. e.g. There are "upstairs" items and "ground floor" items. This was hard to remember in our first game.
Rulebook comment (contains plot spoiler):
During the prologue you may encounter a rule in-game related to something in the rulebook that doesn't have a reference icon. Note: the item referenced already exists in the house tiles. If it's unclear, try to look up what the icon should be.