I am running Linux (Ubuntu 12.04), not a Mac, but I now have this mod running successfully (although with a few minor graphic glitches, similar to issues that I have dealt with in another M&B:W mod and in the [beta] Native game itself).
So:
Some .exe files are simple self-extracting archives and some are genuine executable installers.
The Brytenwalda 1.40 .exe is a genuine installer, complete with License agreement and such.
To install this mod in Linux, I used WINE (it is a compatibility layer, enabling *some* Windows .exe's to run under Linux). There is similar (if not the same) software available for Mac, for example WINEbottler is one that I have read about. I have no current experience with Mac's so I would advise you to research WINE for Mac, perhaps it is easily available in the Mac store (or whatever).
With WINE installed, I simply right-clicked the brytenwalda_sp_edition.exe and chose "Open with WINE Windows Program loader".
WINE creates a "fake" C: Drive (really just a folder). The Brytenwalda install program then ran as expected, and unpacked itself to
home/username/.wine/dosdevices/c:/Program Files/Mount&Blade Warband/Modules/Brytenwalda
So now I had the base mod Brytenwalda folder unpacked on my machine, but it was not in the correct place. I am running the M&B:Warband [beta] through Steam.
The path to my M&B:W modules folder is
home/username/.local/share/Steam/SteamApps/common/MountBlade Warband/Modules
So I simply had to copy (or cut) my Brytenwalda folder from the *fake* c: Modules folder, and paste it into the *real* (Steam) Modules folder, it could then be selected in the Steam > Mount&Blade:Warband [beta] > Configuration options.
After that it was a simple matter to add the 1.41 patch, as that is a .rar archive, which can be easily extracted.
I did have a consistent Crash To Desktop after defeating the first bandit, when the Merchant spoke to me and I clicked "Continue" to try to enter his home (the very first indoor area).
This caused me to try both of the available lightweight texture patches (for older machines), however this did not fix the issue.
I then played around with some of my rgl_config.txt settings (after reading some crash-fix threads) and finally hit a winning combination, allowing me to successfully enter the home and subsequently play this wonderful mod (and save my game).
I do still have some graphic issues, where black graphics are rendered on-screen, instead of transparency. I have corrected that issue before with .dds files for the 1257AD mod (and even for M&B:W Native sky files) so I am fairly confident that I can sort them out again.
I doubt *fingers-crossed* that you will encounter that issue, it seems related to some shader-effects available in DirectX which do not yet have compatibility under OpenGL (but that is pure-guesswork by me).
Good luck
