Although for players this may seem odd thing, for actual developers this can make the game much easier to program as the server handles solely game logic while client handles rendering and other fancy things that don't really matter for the actual game logic. This adds a natural decoupling of graphics and audio processing from logic so even if the system can't deliver the eyecandy fast enough, the game logic does not get bogged down as much because of it (graphics/sound pipeline does not block the game logic pipeline), though this does add small communication overhead between the client and server which may cause lag like effects on slow computers.

More modern take on this is that the clients also maintain some form of understanding of the game logic (mainly things indirectly related to graphics and sound) to allow fairly good network prediction code, hiding away some latency issues (making lag less visible).