Thinking more about this, I'm nearly positive the fruit you originally posted with the added mention of eating green is certainly not Jinhuang. Jinhuang is harvested green then ripens in boxes or sheets for sale. The one you posted now seems to me more like the other mangifera, the Latin name is escaping me now but I grow it also. There are different varieties, one new one becoming popular amongst people who have access is Longan mango. Which is said to be a natural hybrid of the 2 species in the mountains and is now being graded lots. I'm headed now to check my trees for signs of flowering, but only 2 years 8n the ground. This type of mango is well kNown here for being able to eat with green skin while tasting fully ripe. And my favorite aspect is nearly no fiber!
As for best in Taiwan...That's a hard one, everyone has their preference. We eat hard green mangoes that are sour here...I hate them but many LOVE them! Pickled almost in flavour.
Commercially I would personally say Yuwen types are the best as they are big like Jinhuang, but fatter, but have far sweeter flavor, and better texture. More picky in growing though. If people are into the mango scene and can get ahold of less than commercial types, there are hundreds of goodies. The peach types I tend to like, very fruity/citrus like and like Irwin kind of size so good out of hand. But to each their own. I like no fibre, thick skin and firm flesh personally so go for those.
If people are looking for mangoes suited for wet from Taiwan , aim to get varieties grown in mountain side areas of Pingtung, kaohsiung and Tainan counties. The mountains there, especially north pingtung, get some of the heaviest rains around, but note they have relatively rain free winters, albeit quite humid.
For colder types, air for east coast and northern region varieties, but not nearly as many. SW Taiwan is the fruit central of the country.