I wouldn't be so fast to assume that this means problems down the road for Big Sis.
I certainly believe the posters who report having seen problems at other children's parties and so forth. But I never did when my kids were growing up -- it just never seemed to be an issue. All the kids, including little siblings, seemed to get it that the birthday child was the one getting and opening the gifts, and on their birthday, it would be their turn. We were very lucky, I see! Maybe it helped that we made a game out of opening the gifts -- the birthday kid spun a bottle and opened the gift from the child it pointed to, then gave thanks and a hug. Not much of a game, but perhaps enough that it distracted them.
Anyway, I think there is more than one lesson to be learned here, and kids are capable of learning them. For example, Big Sis is probably also learning, or soon will, to let Little Sis go first, get the slice of cake with the rose, or win games sometimes -- just as the adults and older kids in her life do for her sometimes, including letting her unwrap Little Sis's presents while she is still too little to care. Kids get it that sometimes things need to be fair, and sometimes the grownups or siblings indulge you. After all, it doesn't seem like she is insisting on keeping the presents; she gets it that they are for Little Sis, not for her.
She is being indulged, but that doesn't necessarily mean she will learn only to feel entitled; she may also learn about how to indulge others when it's appropriate, because she knows how nice it made her feel. And maybe the girls are learning that it can be even more fun to share their special experiences -- I know many siblings who do. Maybe in three years, their parents will remind Big Sis of how she was allowed to unwrap Little Sis's gifts when she was 6, because she enjoyed it so much, and suggest that now she let Little Sis help unwrap her gifts at her 9th birthday party. She may even think of it herself.
It can go either way, or both, of course. I'm just saying that this isn't necessarily creating a spoiled brat. Handled well, it can also lead to developing a generous heart.