Confusingly, there are three seperate computer games
Virgin Mastertronic released a game based on the book ("Shogun") in 1987 for the PC and C64 among others. This was a strangely abstract simulation game where, as one of the characters from the book, you had to attain the rank of Shogun by gaining followers. The CGA graphics rendered feudal Japan as a very strange, blocky place.
Infocom released an interactive fiction game (with some graphics) based on the book in 1988 ("James Clavell's Shogun"). It was written by David Lebling, one of the creators of Zork. This was one of their last games, released shortly before the text adventure became extinct. The artwork (displayed in a window next to the text output) seems to be pretty impressive for the time. The game was aimed at 16-bit machines including the PC, Mac, Atari ST and Amiga (but was also released for the Apple II).
Finally, we have Shogun Total War, released in 2000 by Electronic Arts. This had no connection with the book, but was a highly complex strategy game featuring huge battles with hundreds of units on screen at a time.
The 1987 game is still my favourite of the three.