All face-offs are not of equal importance
http://faceoffs.net/team/NYR
This site gives better stats then just their overall percentages.
For the most part it still makes them a poor face-off team but if you click on the players, you can see many of the percentages fall off in the neutral zone face-off department, as a team that is mostly because of Hayes, yet Stepan also sees quite a dip in % there.
Moore carries face-offs for the team in the D-zone and on the PK for them most part and that is why they are actually slightly above league average there.
If they want to really significantly improve to near or above league average it would take a player who can win them in the offensive zone and on the PP, which also means not starting Stepan on those particular face-offs. Stepan plays with ? So either that line does not start there or they use a different center just for the draw.
My concern would be more along the lines of Moore not being available to take the D-zone or PK ones as well as him not having very good nights against certain players in that situation.