In response to scientistic (strong
reductionistic/deterministic) claims that we have no free will and that the
self is a delusion I always argue for the emergent, agent self/person being a
real entity and part of the global, prehistoric, and historic community of minds.
That a person is defined by him/herself and his fellow humans by his/her
connection to this domain of dynamic, remembered ideas.
The article above argues that our self remains when we lose our memory. However, it doesn't really provide evidence that the man with the brain tumor has a self independent of his memory. In fact, his memory in large part remains intact. One, he remembers that it is important for him to do work he enjoys. Two, he has not lost that crucial part of his memory that he uses for the various aspects of language he learned during his life, and still remembers.
For me, if he had lost his memory of all the knowledge, beliefs, and values he had acquired during his life, and his memory of all aspects of language/speech comprehension and production, yet remained physiologically vegetatively alive, we could say his self/personness had ceased to exist. Fortunately, we would still respect his humanness and his inclusion as a member of Humankind, as we do a newborn who has yet to learn a language or acquire beliefs and values.
See the following link for a brief discussion of the legal and philosophical understandings of personhood. Those quoted say little to nothing about memory being an essential part of being a human being. Their emphasis is on consciousness (which is reliant on memory) and biological processes.
