Is a multiplexer needed to read from memory
There is implicit multiplexing, created by providing each register with a 3-state output driver, and enabling only one driver at a time onto the bus. That's why you see the \$\overline{\text{RD}}\$ and \$\overline{\text{CS}}\$ lines connected to the Output Buffers in your diagram. The buffers are only enabled when \$\overline{\text{RD}}\$ and \$\overline{\text{CS}}\$ are both low at the same time.