How do you get this far in a meaningful discussion about code without citing - the code?
2012 NFPA 101,
"3.3.81.1* Horizontal Exit. A way of passage from one building
to an area of refuge in another building on approximately
the same level, or a way of passage through or
around a fire barrier to an area of refuge on approximately
the same level in the same building that affords safety from
fire and smoke originating from the area of incidence and
areas communicating therewith."
If the the door leading from Existing to New passes through a proper Fire Barrier, the 'horizontal exit corridor,' i.e. Exit Passageway may be constructed, and connected to other spaces, as merely an Exit Access Corridor.