I would imagine they would be doing this to try to broaden Shenmue's appeal and reach a new crowd. I could be wrong, but if it were just for fans I wouldn't personally see the point of it.
We should get a clearer indication of this with the announcement. If they plan to tell the story from the beginning, I think it’s safe to assume that their aim is to attract a new audience. If it just retells the story of S3 and fills in some of the gaps, it’s for the existing fan base.
As much as I dislike anime, I can see the logic of switching mediums if funding for a fourth game can’t be secured as not only could this potentially bring in new fans to the series, but also remove what I’d consider to be the biggest barrier preventing new players from picking up a fourth game.
At the moment, if they were to release Shenmue 4, anybody new to the series wanting to pick it up would have to play through two twenty year old games and then a third which, by all accounts, is not what the developer had in mind when starting the project. An anime retelling the story of these games would offer what some might consider to be a more palatable option.
Personally I think they’ll struggle to translate the things that make the series so wonderful into a purely visual medium and any audience that such an anime might attract might not necessarily be the kind of people who would enjoy a Shenmue game. Of course, if an anime were to attract a sizable following, it might at least give Yu the leverage needed to secure funding for a fourth game, so every cloud. Whether the anime would then have an impact on the style and tone of future games does worry me though.
Likewise, an anime filling in some of the gaps from Shenmue 3’s story might appease some of the fans who felt short-changed by the game, but I can’t help but feel that the money would be better spent securing a fourth game as were they to pick up at the beginning of the third game and take the story through to the start of Shenmue 4 it would be just as inaccessible as a fourth game for people unfamiliar with the Shenmue story.
I think that if they are going down the anime route, it would only really make sense to start at the beginning and plan to see the story through to the end. Anime is cheaper to produce than a game, but they’ll still want to see a return - and telling a story without a conclusion has very little chance of generating revenue.