Joystick splitters generaly do not work with the more advanced sticks that multi-plex signals onto the same pin.
Originally the gameport was designed for (I believe, but could be somewhat incorrect):
2 axis (analog->8 bit digital converted) + 2 buttons...... all x 2 players. (e.g. 8 discrete inputs)
Each axis measures from 0 to 255, therefore "center" is supposed to be 128, and left or up is 0 and right or down is 255 if you're using a "simple" digital stick connected to it.
Each button is only either 0 or 1. (or possibly 0/255 depending on how the protocol works)
So at most, you can have 4 directions + 2 buttons per player.
However there were MANY ways all the different sticks were multi-plexed onto these inputs. Often times if you had a Digital P1 stick with 4 buttons, the first two of P2 buttons overwrote the 2nd two of P1 buttons (since they were mapped to the same wires) and the other 2 buttons on P2 simply didn't register.
Complicated this by adding buttons and special software, it all gets to be a horrendous problem identifying the inputs correctly.
HAD there been a standard, it's conceivable they could have had at least 36 discrete digital inputs (each bit of each axis byte + 4 buttons) or if the protocol allowed for 0-255 on the button inputs (instead of just 0-1), then as many as 64 discrete inputs total.
However I dont think there was any standard ever made,and now most sticks are switching to USB without all the problems... its just a serial stream of bits arriving (with USB's own ID problems of course--especially with hubs added on).