There are several approaches, and using a CPLD/FPGA isn't a bad one really - they have plenty of IO's and would be easy to implement by just using a schematic editor (or you could learn VHDL/verilog!) with 14 8-to-1 multiplexers.
A completely passive/unpowered approach would involve a huge ganged rotary switch. These are pretty expensive, especially if you've got 14 gangs in one.. So I'm thinking a powered approach is the only way.
You could also do with with TTL logic, 14x 74HC4051 (or HCT) 8-to-1 multiplexers will do (thats 7 for each input line, but double that as you have two Dsub inputs, and two Dsub outputs). As these are analogue multiplexers it won't matter whats an input or whats an output - although clearly your schematic shows that all the joystick lines are outputs (from the joystick) and inputs to your multiplexer.
These are controlled by 3 lines, along with a master "enable" that can disable all connections. The 3 lines are binary 0-7 for your 8 inputs, so you could control these from an Arduino that can just increment this value with a button press, or another TTL IC, a binary counter, so a simple button will change channel from 0, to 1, 2 etc.. Another multiplexer to control 8 LED's indicating what channel is selected and you're done. An Arduino provides much more flexibility in how you select the inputs, and can allow channel indication via simple LED, 7 segment display, LCD module etc.. but probably overkill.
The whole thing could easily be done without having to write any software/code at all, but these days micros, and Arduino's are so cheap, and provide the possibility of adding many more features that if you're well versed in writing code for them, you might as well. But if you're completely new to it all, it can be done with raw logic, all running at 5V (no need for level shifters).