As steveray pointed out the separation would be required between different occupancies, not the fire areas.
However to begin with it would help tremendously if NY has an existing building code (IEBC) for reference. There are several options that would allow the kitchen where the code does not reference or amended the "new" kitchen separation.
The IEBC for example permits "the use or occupancy of existing buildings shall be permitted to be changed and the building is allowed to be occupied for purposes in other groups without conforming to all of the requirements of this code for those groups, provided the new or proposed use is less hazardous, based on life and fire risk, than the existing use."
Additionally it may be useful to know this issue is further addressed in the 2018 IBC provided below.
302.1 Occupancy classification.
Occupancy classification is the formal designation of the primary purpose of the building, structure or portion thereof. Structures shall be classified into one or more of the occupancy groups listed in the section based on the nature of the hazards and risks to building occupants generally associated with the intended purpose of the building or structure. An area, room or space that is intended to be occupied at different times for different purposes shall comply with all applicable requirements associated with such potential multipurpose. Structures containing multiple occupancy groups shall comply with Section 506. Where a structure is proposed for a purpose that is not specifically listed in the is section , such structure shall be classified in the occupancy it most nearly resembles based on the fire safety and relative hazard. Occupied roofs shall be classified in the group that the occupancy most nearly resembles, according to the fire safety and relative hazard, and shll comply with Section 503.1.4
503.1.4 Occupied roofs.
A roof level or portion thereof shall be permitted to be used as an occupied roof provided the occupancy of the roof is an occupancy that is permitted by Table 504.4 for the story immediately below the roof. The area of the occupied roofs shall not be included in the building area as regulated by Section 506.
Exceptions:
1. The occupancy located on an occupied roof shall not be liimted to the occupancies allowed on the story immeditately below the roof where the building is equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1 or 903.3.1.2 and occupant notification in accordance with Section 907.5 is provided in the area of the occupied roof.
2. Assembly occupancies shall be permitted on roofs of open parking spaces of Type I or Type II construction , in accordance with the exception to Section 903.2.1.6