Keybase uses root privileges only for making the magic /keybase directory available, where you can access your KBFS files (the redirector allows different users on the same system to see their own files). Keybase and KBFS run as unprivileged daemons (via the systemd user manager where available).
As giancarlostoro mentioned, you can unpack the .deb file and run the binaries out of there. If you put the binaries in your $PATH, you can even symlink the systemd unit files to your ~/.config/systemd/user and use the systemd user manager to manage your custom Keybase install. Note that the KBFS mount will not be accessible at /keybase, but instead at another location writable by your user (see https://keybase.io/docs/linux-user-guide#configuring-kbfs).
Finally, our build script at https://github.com/keybase/client/blob/master/packaging/linu... builds all components and assets without root and lets you handle the packaging and install after that.
If you have questions or more custom use cases, feel free to join the keybasefriends team to talk about it or make a GitHub issue!