Every child does this to some degree at that age, I think, so I'd chalk this up to age-appropriate behavior, and the concern here is the degree. Perfectionism and being able to outsmart her peers would make it worse. My DD8 does this from time to time, but she also had experience with an older playmate who took it to an extreme, so that gives her a framework for understanding the other side when we point out what she's doing.
In the case of the older playmate, the biggest problem that I noted was that her and her brother were consistently able to manipulate their parents, always getting what they wanted eventually, so she applied the same mindset of always getting what she wanted to play dates... with disastrous results. Both the kid and the parents have lost multiple friendships over the child's behavior. So it's definitely something you want to address, if it's as bad as you say.
In our kid's case, the situation is far less severe, because she learned early on that when her parents say no, we mean it, and when necessary we'll draw a red line where continued badgering will end in loss of privileges for her, and the longer she continues, the more privileges she'll lose. This teaches her how to accept that things don't always go her way. When conflicts arise with her friends over a toy or activity, we (mostly) don't step in and solve the problem, we leave that up to them, but we do coach them about negotiating an outcome that both can accept.
