Ziqi's explanation of what it means that he has lost his 'me' concludes with the previously discussed declaration that the piping of Heaven is the arising of things and cannot be identified as something apart from this arising. Does this satisfactorily answer the question? If it does, it is only after we have done a lot of work in trying to connect the dots. I previously quoted Wang Fuzhi who is able to do so: "If you refrain from setting yourself up as the measure to be compared to the opposing counterpart, what theories of things, what assessments, are not made equal?" Our sense of the otherness of things, our ability and desire to judge between things, these emerge from our doing the same in our experience of self as I-me. This the source of dualism. Things are objects to me because I am an object to myself. Understanding the unity of things as all equally expressions of Dao, the Heavenly, as all "self-right", thus challenges this primal dualism of I-me. It shows it to be an anomaly in the larger expanse of reality.
But whether it is an anomaly or not, is it not that which has naturally arisen and thus likewise "self-right"? It is. But here we have to be careful not to fall into the trap of thinking that because things are, they are 'meant' to be. To follow Zhuangzi's paradigm we must leave intentionality behind; nothing is 'meant' to be; things just happen. I am tempted to call them "accidental", but this may be as mistaken as saying they are purposeful. Between these two extremes, perhaps it is enough to say that nothing is sacrosanct; nothing is holy; everything is under review. Killer bacteria are themselves "self-right", but having obtained the ability to kill them, killer humanity is "self-right" in doing so. If the apparently 'accidental' arising of the I-me dualism is similarly revealed as detrimental to human flourishing, then this too is subject to amelioration. (It goes without saying that any idea of a 'Fall', and thus a need for redemption, is entirely foreign to this paradigm.)
Thus, the I-me form of selfhood comes under scrutiny; simply because it is a given does not mean that we need resign ourselves to it in more than we should resign ourselves to an inflamed appendix. If we find it problematical, and it is within our capabilities to alter it, then we are free so, though not as a moral or redemptive imperative.
You can check out Scott's writings on Zhuangzi here.