Does this wiring pattern for a DB9 cable exist as a standard cable?
That is a standard null modem cable with handshake also known as crossover.

It is used to  connect two DCE devices or two DTE devices together.

DCE (data circuit-terminating equipment)  .... example: modem
DTE (data terminal equipment)  .................... example: computer



TXD - transmit data
RXD - receive data
RTS - request to send   
CTS - clear to send
DTR - data terminal ready
DSR - data set ready