Chessmaster is not available for Linux but there are plenty of alternatives that runs on Linux with similar functionality. The best Linux alternative is Lucas Chess, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 25 alternatives to Chessmaster and 11 are available for Linux so hopefully you can find a suitable replacement. Other interesting Linux alternatives to Chessmaster are XBoard (Free, Open Source), ChessX (Free, Open Source), DreamChess (Free, Open Source) and Shredder Chess (Paid).
XBoard, also known as WinBoard on Microsoft operating systems, is a free graphical user interface client developed by Tim Mann that is compatible with various chess engines that support the Xboard Communication Protocol such as GNU Chess.
DreamChess is an open source chess game featuring "Dreamer", a moderately strong engine. Any XBoard-compatible chess engine (Crafty & GNU Chess) will work for varying degrees of difficulty. Includes 3D OpenGL graphics and various board sets.
Winboard works more as a graphic front-end for several different chess engines included with the game, as well as for several chess game modes. These include not only player vs player or human vs computer competitions, but also games played online and even by email.
Jin is an open source, cross platform, graphical client for chess servers, written in Java. Jin can run either as a standalone application (available at this website) or as an applet, directly from your browser (available at the chess server's website).
Arena is a free Graphical User Interface (GUI) for chess. Arena helps you in analyzing and playing games as well as in testing chess engines. It runs on Linux or Windows. Arena is compatible to UCI and Winboard protocols.