I look at it is like this:
Shenmue 3 has been looking for publishers and a method of funding for years. Obviously no one has taken to the plate, probably as, "No one remembers Shenmue," "It's only wanted from a vocal minority," "Financial loss," etc.
Sony heard the fans, but like many others probably was hesitant to put millions of dollars here, so to prove investment, it's asked for fans to "Put their money where their mouth is," which is probably the only way Shenmue 3 was going to show there were people who'd actually buy the thing rather than taking a blind risk worth millions of dollars.
Fans gets the game for a cheaper-than-retail price and get to be involved in active development and feedback of the game, as well as get goodies. Yu gets to have data that fans will support Shenmue and gets a platform to interact with his core fan base more closely. Sony gets sales date and 'proof' of worth to be able to put some funding into it.
There literally is no lose here for anyone involved, they're even being transparent of this fact in less than 24 hours since the Kickstarter launched, no money has been taken yet and there's plenty of weeks to think on it and let people who want to be part be part. The only people that are upset are those that want to be upset or take issue asking, "What's the point, this feels slimey," not knowing the purpose of the term "Kickstarter" and not understanding why Sony, 'couldn't just fund it themselves.' It's not couldn't here, it's wouldn't, because there is very slim chance this game will sell like hotcakes, and they know that, this is likely going to be coming up as a loss for them, BUT it allows something fans really want to happen, and allows fans to both be more directly involved AND put their money where their mouth is to support and prove there's interest, while getting goodies and lower prices for those who want them and want to support.
This wouldn't work with every game, but it makes sense for Shenmue 3, and if they didn't do it this way, then it'd probably wouldn't happen. It's also probably the smartest way to tackle, "Shenmue 3", honestly, rather than making it hush-hush anyways. Shenmue 3 is happening because of fan demand, so get the fans involved, and those involved can help leave feedback and relay stuff directly to the creators and the team, as well as answer questions the team wants to know about going forward with the fans.