Depends
If your Oceanic route starts in the NEW YORK Oceanic area, the NOTAM applies - your Flight Plan Route (as cleared) is your cleared route, without further ado, doesn't matter whether you transit Santa Maria or Gander after the initial portion through NY Oceanic area.
If your Oceanic route starts in Gander Oceanic (after you have transited US FAA airspace), then the Gander Oceanic Clearance procedure applies, not this mentioned NOTAM.