The pinout looks standard, there's a chance they did something screwy but I don't think that's very common these days. If they used a standard relay for the fan did they use the same for something else? You might be able to just yoink them from the horn or something less essential for testing. Like others said the main thing is match or exceed the current rating.
Don't buy something like that on Amazon though. Tossing that part number into RockAuto and they have genuine Hyundai for $58 or Hella for $8.
Edit: The Hella shows the pinout, compare it to the pinout on one at the store but that looks conventional to me. Just check the fuse box to see if there's a space for the extra pin most generic relays have.
Hella:
Generic:
Edit 2: looking at it again the Hella relay has a protection resistor as well. I'm not sure if the Hyundai one has that or not but it might be worth at least calling around to try and get a proper aftermarket one first before trying a fully generic one.