As someone who bought the original on Dreamcast day 1, Imported Shenmue II day 1 and double dipped on Xbox day 1, I've been dreaming of this announcement for the last 14 years. The franchise was dead and mostly forgotten with only a few diehards perpetuating the demand for a third installment. Still, there was an opportunity for some publisher or platform holder to gain the undying loyalty of a core subset. The folks like Gio and Boyes at Sony knew this and have obviously been working with Yu find a way for him to complete his story.
The kickstarter approach accomplishes three things that outright funding the project would not:
1. It gauges the current interest and willingness to purchase this expensive yet very niche IP, in the process offsetting a portion of development costs. This is a passion project with very low profitability likelihood, and a fairly unique scenario, so asking fans to contribute to the project proportionate to their desire to see it exist is not completely uncalled for. We won't be seeing this approach for Assassin's Creed, or COD, or other high end IPs, and it's not even setting a precedent since Bloodstained and many other niche games already used crowdfunding to prove interest for investors.
2. It allows fans to more directly engage with the creative team, as well as get exclusive memorabilia like signed artbooks, jackets, and scripts. In this sense it mostly serves as a very early pre-order system with similar bonuses.
3. Most importantly, by presenting it on a very public stage with Yu on hand, it guaranteed that the Kickstarter would be funded, credible, and attention garnering. How do you drum up interest in a dead franchise? You create headlines like:
"Sony reaches $2m Shenmue III game target on Kickstarter within hours"
http://www.bbc.com/news/technology-33144515
"Shenmue 3 becomes fasted game to raise $1 million on Kickstarter"
http://www.theweek.co.uk/64011/shenmue-3-becomes-fastest-game-to-raise-1m-on-kickstarter
This prompts the uninitiated to look into Shenmue and learn more about it, seeing what the fuss is all about and helping generate buzz and excitement. Imagine if Sony had decided to outright fund the game, or KS didn't exist. Then instead of those headlines we'd be reading stuff like (hypothetically): "Sony inexplicably funding the third installment in a franchise no one wants" and the naysayers would latch onto that notion without the KS- provided proof of demand to back it up.
Without the Kickstarter proposition this game would still be dead, so for that I'm thankful.