This isn´t a private purpose, although saving wildlife is very close to PWilliam´s heart - the Duke has been asked by the british government ("HM´s government"!) to do this trip! In that regard meetings with vietnamese officials were essential.
The post that you refer to was for the trip to Kenya, not the trip to Vietnam.
The trip to Vietnam is not at the request of the UK Government, although they would have supported it. He has travelled as the President of United for Wildlife. The reason to speak to Gov ministers is to talk about legislation to prevent ivory trafficking.
It has been a busy couple of days - here is the CC for 16/17th November
16th November, 2016
The Duke of Cambridge this morning arrived at Noi Bai International Airport, Hanoi, and was received by Her Majesty’s Ambassador to the Socialist Republic of Vietnam (His Excellency Mr Giles Lever).
His Royal Highness this afternoon called upon Mr Nguyen Xuan Phuc (Prime Minister of the Socialist Republic of Vietnam) at No 1 Hung Vuong Street, Ba Dinh District, Hanoi.
The Duke of Cambridge afterwards called up Mrs Dang Thi Ngoc Thinh (Vice President of the Socialist Republic of Vietnam) at No 1 Hung Vuong Street.
His Royal Highness, President, United for Wildlife, later visited Hong Ha Primary School, Lan Ong Street, Hanoi, and
subsequently met Vietnamese conservationists at Aha Café, Thuoc Bac Street.
The Duke of Cambridge afterwards visited Ngoc Son Temple, Hoan Kiem Lake, Hanoi.
His Royal Highness this evening held a Reception at the Sofitel Legend Metropole Hotel, Hanoi, for young Vietnamese leaders from the worlds of art, music, media and business.
17th November, 2016
The Duke of Cambridge today carried out the following engagements in Hanoi, Vietnam.
His Royal Highness, President, United for Wildlife, this morning attended an Illegal Wildlife Trade Conference at the Lotte Hotel.
The Duke of Cambridge, President, United for Wildlife, afterwards attended a Meeting with delegates from the Association of Southeast Asian Nations, at the Lotte Hotel.
His Royal Highness this afternoon received Mr Vu Quang Hoi (Chairman, T&T Group) at the Sofitel Legend Metropole Hotel.
The Duke of Cambridge, President, United for Wildlife, subsequently received Mr Yue Lei (Senior Vice-President, Sanpower Group).
His Royal Highness, President, United for Wildlife, later visited Vietnam Television Studios