In the games directory, I found a folder named "rom", but the files are all .bin and won't run on MAME.

Those are not the correct files. You need .zip files from the "goodies" section. Download the Mac OSX goodie and unzip that folder. Then, use a file opener like 7-zip to open up the remaining folders until you find the rom names: lastbld2.zip and neogeo.zip. I hope this helps.

EDIT - It appears that The Last Blade 2 does not have goodies like its predeccesor does. Therefore, you can only play the actual port / Windows version of The Last Blade 2.