In New York, parties can cross nominate. This means that the single issue more ideological parties pick their candidate. And then if the Democrats or Republicans failed to nominate that candidate, they pose the risk of splitting the vote. In reality what these parties do is attempt to enforce ideological purity on the Democrats and Republicans. The Conservative Party plays this role on the right, or at least is supposed to do do. The working families party has been doing a bang up job of this on the left recently, but is controlled by the public employee unions. Cuomo probably wants a left-wing party under his control.
Cuomo already has the Democrat, Independence, and Working Families nominations.
Maybe he should help the Liberal Party regain ballot status. He was their nominee in 2002.