No, it does not cure the diseases, but it does alleviate the risk of pregnancy when a future pregnancy could be life threatening.
Procedures that induce sterility are permitted when their direct effect is the cure or alleviation of a present and serious pathology and a simpler treatment is not available.
This would fail all three criteria: the tubal ligation would not cure anything; it would not alleviate a present pathology (the woman's present pregnancy is apparently not the problem); and there are other ways to avoid pregnancy other than intentionally destroying healthy reproductive organs.
However, the article says that "Millers case did clear the high bar for sterilization set by the Ethical Religious Directives." That can only mean that the tubal ligation is not directly intended for sterilization, but for some other purpose.
I'm just wondering what that could possibly be. The only thing I can think of would be a disorder of the fallopian tube itself. Cancer?