**THIS REVIEW CONTAINS MILD SPOILERS**
tl;dr: It's a good adaptation that tries to quickly tell the story of the first two games in 13 episodes but misses what made Shenmue what it is. You are free to watch this without playing the games but doing so may make the story, characters and world feel less impactful and interesting.
As a fan of Shenmue since its release (or close to) seeing an anime of it is welcome, but also quite confusing. In my opinion, Shenmue is a game that is about the minutiae of everyday life that you should really experience for yourself at your own pace. Even if you can't appreciate that factor, it still is an incredibly unique experience for everything it has to offer. A semi-open world game set in a rural 80's Japan where you can walk, talk and interact with pretty much everyone and everything made in 1999! The game oozes soul from the moment you start exploring the world and it just keeps it up, it's incredible to think a game like this could exist back then and that's one of the things I love about the game.
Seeing an anime of Shenmue feels like it is cheapening the experience, like most (keyword "most") video game adaptations the source material is always the best way to experience it, and Shenmue is no exception. If you are interested in Shenmue in anyway you should always play the games as they are what Yu Suzuki wanted and a majority of fans have experienced. That is to say, watching the anime is by no means a substitute for playing the games. This is an anime made for the fans (and almost made BY the fans) and if you're not a fan you probably won't enjoy this anime that much. It will seem rushed, confusing and overall not something that represents what Shenmue is all about.
However, the Shenmue anime isn't entirely terrible. I feel that it is around a 7.5. The anime gives a cleaner, faster and to the point experience of showing the viewer the story, characters and world of Shenmue. Letting you experience around 40 hours of content in 13 episodes and so far (4 episodes) it has done a good enough job.
The anime even goes as far as giving more content. Scenes such as the martial arts tournament that occurred the same day Ryo's father was killed at the beginning of the game was added to the 1st episode, Ryo also talks and hangs out with his friends (well Nozomi) more often than he did in the game, more scenes showing Shenhua (the mysterious girl who seems to know of Ryo's impending journey) in her village were added and even backstory relating to the inner workings and discussions of the underground crime syndicate as Ryo interacts with them during the game were added. The anime feels like it knows that it can't replicate the games 100% and instead opts for a faster and skewed perspective on the plot, adding interesting changes to the show for better or for worse.
The animation is decent, fights are few and far between (much like the game) but when they occur they hit hard. Punches and kicks feel and sound POWERFUL and make each encounter quite entertaining to watch, with QTE's also becoming quite the display of Ryo's strength and dexterity instead of loud beeping in your ear as you fail to press A on the Dreamcast controller in time, seeing Ryo fall to the floor wincing in pain due to your own mistake. The art is...fine, it's pretty standard for modern anime of the time and portrays each character well enough to recognize them but it's nothing incredible, it does suffer from the horrible 3D background characters in certain shots, but it doesn't entirely detract from the show.
Voice acting is great. Making emotional and dangerous scenes feel more impactful, serious and is honestly better for it. The Japanese dub for Shenmue even back on the Dreamcast was quite good and this anime even has the same voice actors for Ryo and Lan Di giving the exact same performance as they did 20+ years ago.
As for the story; it feels rushed and it's an understandable compromise, while it does get to the point faster it misses out on the smaller parts of the game. Scenes such as the tattoo parlour and sneaking into warehouse number 8 are removed in favour of speeding up the plot. It's not bad and you could argue removes some of the "fluff" the original game had but it does make the overall pace of the show feel faster and and misses the point of Shenmue being a slower experience. I do also think that when told directly as this anime is doing, the story will seem subpar, perhaps even cliche for the average viewer.
Characters are also a mixed bag. While some are made to be less important than they are. Such as Tom, the man who sells hot dogs in the first episode who is a valuable friend to Ryo in the first game, is regulated to one conversation in the first episode and that's it. Others such as Nozomi (Harasaki), Goro and Fuku-san are given much more screentime in the anime, even going as far as having additional scenes not shown in the games, I actually really like this change since it makes the characters feel a lot more important to the plot and to Ryo.
The music is probably the biggest disappointment for me. I love the original tracks that the games had and wish I could've heard more of them replicated or remixed here, but instead this anime has pretty forgettable tracks I find, serving as nothing more than background noise to listen to while scenes play out. In the Ace Attorney anime, a majority of the music from the games was remixed to play when they would've in the games, it's a shame that Shenmue didn't try and take this approach with the anime and the only tracks from the games that I have heard so far being the main theme and Shenhua's theme.
Overall, the anime is not bad. I will say that if you have any intention of watching this anime you might instead want to look into the games instead and watch this afterwards to compliment it. However, if you're fine with watching it then Shenmue is a decent attempt at adapting the games for the viewer removing "fluff" and getting straight to the point of the story.
Pros
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Mostly an accurate and faithful retelling of the games (with some caveats)
Original VA's for Ryo and Lan Di
Animation is good enough
Additional scenes not seen in the games
Cons
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A small selection of music from the games
Side characters lose a lot of spotlight when they were integeral to the games
Plot has to be rushed so it can fit into 13 episodes
Multiple changes to the story could be seen as differing too much from the source material