Yes, there are several options for excluding files and directories. There's the --exclude option to exclude a file or directory. There's also the --exclude-from option that lets you specify a file that contains a list of files and directories to exclude.
There's not much point in backing up games that are easily downloaded again. Just backup the saves and settings.
It's a known issue. They are working on a fix, but it's not ready yet. It will require an external JavaScript library though.