You need to convince yourself that Rx or Tx (and variants like RXD, TXD) are signal names, rather than indicating direction of data flow. The descriptions of the pins in that you quoted do indicate direction by the use of the words input and output. An output generally connects to an input.
When you connect an SPI "slave" and a "master" device together, you connect the MISO pins of the two devices together, likewise the MOSI pins together, and same again for the CLK. On one of those devices, each of those is an input and on the other, an output (e.g. MISO is an input on the master device and an output on the slave).
Usually, when connecting a UART type perhipheral to a microcontroller (etc.), you likewise need to match signal names, so RX to RX and TX to TX. This moves the "TX" data from one device to the other. The exception is when connecting two peer devices together (e.g. the UART Tx/Rx pins of two microcontrollers so they can talk to each other). Think about why.