The idea was using Game Port so you could use it in DOS, W95/98, etc without needing a specific driver.
So I think the best would be to use one of those 8bitdo SNES receivers, because they already allow pairing to (according to their website):
8BitDo controllers and arcade sticks (excluding 2.4G controllers)
Xbox Bluetooth® controller, DualShock 3, DualShock 4, DualShock 4 Pro
Wiimote, Wii U Pro, Switch Joy-Cons, Switch Pro
Thats a lot of supported control pads with just one receiver.
Would be great to find some info about an arduino SNES to Game Port. Currently I don't know anything about SNES controller output signals or DB15 input signals.