Very interesting find!
If you want to find the location today on a map of your choice, it's the location of Herricks High School and the surrounding houses.
The "Links at North Hills" development just to the east is the land which was The Links.
@Paul, respectfully, the "Motor Parkway" referenced in the course map is Vanderbilt's Long Island Motor Parkway. The Northern State Parkway is a different roadway.
The LIMP ran on the south edge of The Links, and curved up and around this property. You can see it on a map today; the right of way is not continuous today. It headed east and cut south right in the middle of Wheatley Hills Golf Club.