"The state had argued that the names of lottery winners must be disclosed to ensure that prizes are distributed fairly and that winners are not related to lottery employees."
First, they know who they are writing the check to so the whole "not related to lottery employees" part seems rather bogus.
I thought the whole point of disclosure was publicity, but this got plenty and being able to gamble without telling the world you won probably will sell more tickets anyway which is the whole point of the publicity.