Do Matrixists actually believe that the reality we live in is a computer generated simulation?
No. Matrixism looks at the “computer simulation” aspect of The Matrix as a metaphor for the rules, norms and values of our current society. This metaphor also refers to hyperreality (i.e. television, radio, internet, etc.) which effects people in much the same way as raw (i.e. real) experience. The subject of hyperreality is addressed in the book Simulacra and Simulation by Jean Baudrillard. A hollowed out copy of Silmulacra and Simulation makes an appearance at the beginning of The Matrix.