Are United4Wildlife and EarthshotPrize not primarily his own initiatives? So why the 'at the request of the government'? It seems more likely that the government was asked by William's entourage to request him to go...
The full press release stated that the Government requested he go to participate in the UK National Day take over of the Dubai Expo to promote "Global Britain" which is more than just his wildlife charities. It also mentions that he will be meeting with government officials.
It seems likely that the FCO and KP co ordinated the chance to do both - to promote UK interests officially post Brexit and the chance to promote Earthshot.