Publisher's blurb: "Beyond the Edge uses a gaming system called "Evolve/Beyond", an innovative method of allowing you to keep all that you have obtained during each game for the next, allowing you to have individual stories that are specific to your character and which progress independently of your allies."
For me it sounds more like the character development in a RPG like D&D. You have an adventure (game) learn some new skills or get better in something and then you embark on a new mission. That Mission can be everywhere. In this case at your game or the game of a friend.
The component list includes stickers and envelopes. It sounds like legacy to me.
you can even take your ship, captain, and missions and jump into other players' games, creating an ever-evolving gameplay experience
That isn't the same thing as legacy or campaign.
That bit is somewhat novel, I admit, but one thing doesn't preclude the other. Besides, it can be troublesome. How is the game going to handle characters of different experience levels? Do you just take your level-ten character to a game with a bunch of level-two heroes?