Unfortunately, you won't be able to run Malwarebytes Anti-Malware until you upgrade your operating system. Snow Leopard is just too old, and the application no longer supports such outdated versions. Additionally, there's also no way for you to download older editions of Malwarebytes and it wouldn't make much sense to do that as being up-to-date with the latest threats is the only way for security tools to effectively protect your Mac.
So, if you want to use Malwarebytes Anti-Malware on your Mac, you will need to update to Mac OS X 10.9 or a newer version of Apple's operating system.