I installed Warband on a Mac and when launching experienced the attached error.

This occurred when executing the launcher, i.e. prior to selecting a module.

Reinstalling did not help.

The requirements for the game are as said X.9 but I'm already assuming you modified the plist file(s) for the "minimum system version" since you got to that error. I haven't tried this game on my X.6.8 laptop yet but I did modify the plist files to work on my X.8.5 desktop(I could upgrade to Yosemite but I'm just waiting for Gameranger to update) and it did seem to run there.

But the reason it bonks in X.6.8 is because they didn't put new standard c++ libraries in until Lion. But even if you just copied those libraries over(a hack you do at your own risk) it may still crash. I should probably check it on mine since I copied over 2 library files from my mountain lion system(once again a hack that you make at your own risk - I would not replace any files!!!). The 2 files I copied over did manage to get Retro City Rampage DX running though but that's a much smaller game.

Note that the two files I used from the newer OS were:

libc++.1.dylib
libc++abi.dylib

Don't take this as a statement that these 2 alone will make it work though and the more it requires the more likely it is to cause problems.

Edit:

I checked and it started wanting frameworks so I'm not going to try further(well the launcher did), the actual game itself just threw up an exception so that won't work either. Plus anytime I've started messing around with frameworks it's iffy it will the computer will start and I might have to boot in safe mode/boot from CD(It's happened before).