New York State Absentee Ballot Application
For the June 23rd primary this year, Cuomo ordered that absentee ballot applications be sent to every voter on the voter rolls in NY State. I got one, but ripped it up, because I voted in person.
The sample ballot you posted is the type that is found at the polling site for people to look at before they go into the booth. You have to sign under your name in the alphabetical book they have, and you are then given your own numbered ballot. The number on the ballot is written down, along with your name on a separate list. There are no absentee ballots for this years election posted for download. I could not find any, just the applications to request an absentee ballot to be sent to you.