Scott is right and you shouldn’t be using sudo to run Lutris.
But that isn’t the issue here, your distribution seems very out of date. I believe you are running Mint, is that right? If so, make sure you have updated to Mint 18 as we have introduced features that won’t work on older versions of Mint (or other distros for that matter).
Yes, I tried it as a standard install first and it simply wouldn’t execute (no errors either) from my menu .
Then downloaded the tarball and tried it manually. No dice
No, Mint 17.1 is not supported, the only Mint version to have the features we use is the current one, Mint 18. It’s not about the graphics card, it’s about the version of Gtk shipped with Mint.
You shouldn’t need to backup everything and reinstall your OS, a simple upgrade should to the trick. (Well you should always be doing backups but that another story )
If you are running a supported distro, you should be able to use the deb packages. We strongly discourage installing Lutris from the tarball, this is unsupported as well