Nate Birkholz has posted the Mac Myth III system requirements in the Myth Village forum. They read:

• Mac OS 9 or Mac OS X v. 10.1. Mac OS 9 users also need Apple's OpenGL 1.2.1 update and GameSprockets 1.7.5. (Included)
• 400MHz G3 processor (600MHz recommended)
• 128 MB RAM
• 348 MB hard drive space (500 MB required for optimum performance
• OpenGL video card with a minimum of 8 MB of video memory (16 MB or more will greatly increase performance).
• 56K or faster connection required for on-line play
• QuickTimeЩ 5 or higher (Included)

Birkholz also added, we have actually run it on a 350Mhz iMac DV, with all the graphics dialed down, but lordy, I wouldn't recommend it.