That's the thing, they had to work for them. She just had them. One could argue that she is more powerful due to the nature of her grandfather raising her, being the first to enter the dream state and eventually when Gunkind comes into play, but the lack of seeing any work does get a little annoying.
Well, okay, maybe. I don't mind it, but I see your point.
The problem is moreso her doing whatever and stuff happens and WAT WAT WAT. John got a game and started to play it, eventually getting caught up in an adventure. Rose and Dave are in similar situations, with somewhat clear goals and reasons for what they do what they do. Jade has no reason or purpose. She ferries around objects for time travel for who the hell knows and generally just chats around and feeds her dog. Why does she do this? Who the hell knows. I just can't sympathize with a character when you know nothing about them.
John got a game, started playing it, and then discovered that his father has been monitoring meteor activity for who knows how long, and apparently knew all about the adventure. Rose wanted the thing to resurrect her dead cat, to inquire about something he apparently told her years ago, only to discover that her mom has been trying to do just that in the laboratory next door with Sburb spirographs on the walls. Dave... Well, okay, he seems to be in it mostly because he's friends with the other kids, but his brother still seems to know something about it. EVERYONE'S involvement in this temporal clusterfuck is caused by some stable time loop or another. "Stuff happens and WAT WAT WAT" is pretty much Andrew's modus operandi.
As for Jade's motivations, the obvious one is that she wants her friends to win the game and save Skaia or whatever. She just knew about it beforehand, thanks to her Skaia Cloud Visions. Chatting around and fighting their guardians, as well as struggling with their inventory systems was what EVERY kid did before moving to the Medium, by the way, and if the gray bars in the Trollian timeline window mean that, it will happen fairly soon. I expect she'll then start fighting imps and get her bed tossed into the ocean by John, just like everyone else.
Mary Sue's are not neccessarily bad things. Many of the best works revolve around a well executed Mary Sue. Gandalf, for example, is pretty much a posterboy Marty Stu (male version of Mary Sue) but he is executed well within the story and thus it works.
The reason the words "Mary Sue" bring so much hostility is largely because they're not easy to do properly, and inevitably every poor fanfic writer screws something up with a poorly executed Mary Sue.
The TVTropes people can't agree on anything about the term "Mary Sue", except the negative connotations. It could be argued that Gandalf can't be a Mary Sue
because he is well written.
And it's not like other people in the Lord of the Rings were very flawed, either. Bilbo, Tolkien's ACTUAL author avatar was the only person in the history of the universe to willingly give away the One Ring. Aragorn is the True King of Gondor, and successfully mind-wrestles Sauron over the Palantír. Gandalf is powerful, but he doesn't stand out as much as poorly characterized fanfic people.