I echo others here who have said there is no game quite like Shenmue; it truly is one of a kind. However, depending on exactly what it is that you enjoy about the series, you can find games that scratch specific itches. For instance:
If you like how "real" the townsfolk feel, then the obvious game to play is The Legend of Zelda: Majora's Mask. Like in Yokosuba, the inhabitant of Clock Town each have their own names and schedules, and have their own stories going on in the background independent of the player. Majora's Mask is much more "gamey", as the villagers' problems are more pressing, and it's your goal to solve them— not to mention, um, it's a Zelda game— but this game has some of the very best incidental NPCs around.
If you like the "serious, but low-stakes" tone, then the Kyle Hyde series— Hotel Dusk: Room 215 and Last Window: The Secret of Cape West, both for the Nintendo DS— could be what you seek. In his games, Kyle investigates mysteries that really only matter to him, while uncovering other secrets and helping people along the way— which feels broadly analogous to Ryo's quest for revenge taking a backseat to more immediate and pressing concerns. Of course, these games are more akin to traditional adventure games and are thus a more guided and linear experience. As a side note: Last Window was never released in North America, but it was released in Europe, so you'll need to import a copy. But the DS is region free.
If you like exploring well-realized places that feel "lived in", then realMyst, Gone Home and other games of their ilk ("walking sims") might be up your alley. This is less about Shenmue as narrative experience and instead looking at it as an atmospheric experience; the curiosity it can invoke with how all its drawers and cupboards can be opened, each revealing unique contents and that frequently give a little glimmer of a character's personality. Myst-likes and walking sims are all about that low-key detective work, investigating your surroundings and piecing together— in your head— what it says about the people. Of course, that's also the biggest thing setting it apart from Shenmue: you never actually meet any other characters face-to-face. But if environmental storytelling is your thing, this is a very rewarding genre to look into.