There is no “case” here in NY. Nobody in NY is (currently) arguing that same-sex marriage is constitutionally required by the NY constitution or the U.S. Constitution.
They’re just trying to pass it into law in the legislature.
The only “case” would be if opponents were to argue the NY constitution or U.S. Constitution FORBIDS same-sex marriage, which would be a tall order, to say the least.
If this law passes, there will be a case as Traditional Marriage advocates will sue.
And it will be a tough case to win.
At that point the SCOTUS will Roe v. Wade bans on gay marriage.