The application form for the year Walker won, 2019, says,
"2. Eligible Books
a) The Prize is open to writers aged 50 or
over at the time of publication, for their
first published work of fiction or non-
fiction. Proof of date of birth will be
requested at the point of judging.
b) The writer must be a citizen of, or
resident in, the United Kingdom or
Republic of Ireland. The book must be a
unified work. collections of short
stories, novellas, poetry and drama are
not eligible.
c) Books originally written in another
language, and translated into English,
are not eligible.
d) All entries must be published for
the first time in the UK or RoI within
the calendar year 2018. Previous
publication of a book outside the UK
does not disqualify it.
e) Self-published books are not
eligible.
f) A book submitted on behalf of an
author who was deceased at the date
of publication will not be eligible for
consideration."
(a) doesn't mention self-published books one way or the other, so the obvious reading would be that TSP wouldn't be eligible.
Edit: So not terribly different from the rules as they now stand, except now they explicitly state that a self-published book counts as a previous publication, thereby making an author ineligible for the prize. To give Walker the benefit of the doubt here, that may not have been clear when Walker applied: otherwise why would the RSL have revised the rules? So Walker may be able to claim she made an honest mistake when she applied.