The binary from the Dolphin website was built with a newer version of libc6 (2.15). The thing is, Debian's "latest" version of libc6 is older than 2.15. You can see that updating libc6 on your system did nothing. Debian is known for being a "stable" Linux distro, and by stable they usually mean old-as-dirt software (okay, maybe that was uncalled for, but what can I say, I'm not a fan of Debian :p). You can either manually update the software yourself (compile from source), try using the Debian testing or unstable repositories to update said software, or possibly see if you can compile Dolphin yourself with these instructions: https://code.google.com/p/dolphin-emu/wiki/Linux_Build
If you still run into trouble, you might as well try using the latest version of Ubuntu (since that's what the Dolphin buildbot uses for Linux builds, I assume) or Mint; either is certainly more user-friendly to newcomers. Once you get some more Linux skills though, consider the power of Slackware
If you still run into trouble, you might as well try using the latest version of Ubuntu (since that's what the Dolphin buildbot uses for Linux builds, I assume) or Mint; either is certainly more user-friendly to newcomers. Once you get some more Linux skills though, consider the power of Slackware