The reason that they don't accept reservations by email is probably that they want to provide immediate feedback when they can't meet a specific request. (e.g "Sorry, but we can't fit you in at 7.30 However we do have a table free at 8.30. Would that be acceptable?"). If they entered into correspondence by email they'd be left holding tables for people who might be prepared to accept the alternative time but who might not. (While they were waiting for a reply, which might never come, they could receive an enquiry from someone else who would like to take up the vacant slot.
[Should they let the second enquirer have the booking, and risk annoying the first person they'd offered it to, or hold the table open for the first person (who might not come back to them, leaving them with an empty table)?]
The restaurant will have the same (or greater) reluctance to get involved in snail mail correspondence. If you insist on writing you should simply address the envelope to 'Reservations' but it would make far more sense to phone them. International calls don't cost that much these days:
00 1 212 965 1414
Chris