New Hamsphire Plumbing Code is the International Plumbing Code 2000 if I am reading correctly:
Don’t know when it was adopted, where it applies, or under what plumbing code this structure was built.
Only the plumbing code that was in effect at the time of construction applies here.
That said, International Plumbing Code (commercial) and its International Residential Code (resdiential) counterpart allows for a minimum main vent of 1 1/2" as shown…although for your region it should have an increase in size to at least 3" to prevent frost closure where it exits the structure…
And as jason1 said, there are required clearances from lot lines, openings, and grades just as mentioned.
But under the IPC and IRC a through-the-wall vent is not permitted to be the only vent for the structure.
Section P3102.1 of the 2000 IRC requires that EVERY BUILDING shall have a stack vent or vent stack and such a vent shall run undiminsihed in size and as directly as possible from the building drain to “open air above the roof”.
A side wall vent is not allowed as the ONLY vent in a structure according to NH plumbing code.
But again, it depends when this installation was permitted and done.
It may have met ‘code’ at the time of installation.