The comparison with GTAIII is not so good. There really is no equivalent to the madness that is Shenmue. There are some elements of it you can find in other games before and after it, but the whole package is pretty much unique to it.
Its core idea is to make a realistic world with a realistic adventure in it. The scale of the world had to be reduced (most of the action takes place in a small neighborhood in Tokyo - technically in Yokosuka, which is part of Greater Tokyo) to allow for an amazing level of detail. You can open all the closets and drawers in your house and they are all full of stuff that makes sense (by opposition to the random junk cluttering an Elder Scroll game), there is an ungodly amount of recorded dialogues for the people of the neighborhood, everybody is going about their daily routine and, very importantly, the game has a "realistic" approach to time and not only in term of night/day cycle and weather. In the main narrative, at some point, you get an appointment with another character 'tomorrow at three', so you have to kill time until the next day at three. That sounds ridiculous, but that highly contributes to the unique feel of the game, to the credibility of its world (I think you can speed time up or go nap to warp ahead, so some concessions were made for playability!).
This is a game where you kill time at the arcades, where you go ask you neighbors if they have seen a black car around, where you are in love with the local florist, where you grabe a coke from a vending machine, where you need to work a blue collar job to gather some info about a gang... it is unique and uniquely ambitious.
