The marvellous backup Gem isn’t available as a pre-packaged RPM and as Fedora is missing a simple =build_essentials=-Style meta package, there are some dependencies you’ll have to provide, before you can install it via Rubygems:

sudo dnf group install "C Development Tools and Libraries"
sudo dnf install rubygems ruby-devel patch redhat-rpm-config libxml2-devel

# and you're good to go:
sudo gem install backup

Fore more details, check the Fedora Rubygems page.