Thanks everyone for their input!
Credit goes to @ThanosApostolou. Once I removed steam-launcher it is not showing up in Software Boutique. This also removed the Application links.
I removed ~/.steam and ~/.local/share/Steam from my system but I still found the following.
~$ sudo locate steam
/etc/apt/trusted.gpg.d/steam.gpg
/etc/gufw/app_profiles/steam.gufw
/etc/gufw/app_profiles/steam.jhansonxi
/lib/udev/rules.d/99-steam-controller-perms.rules
/usr/bin/steam
/usr/bin/steamdeps
/usr/lib/steam
/usr/share/app-install/desktop/steam:steam.desktop
/usr/share/app-install/icons/steam.png
/usr/share/applications/steam.desktop
/usr/share/doc/steam
/usr/share/doc/steam-launcher
/usr/share/icons/hicolor/16x16/apps/steam.png
/usr/share/icons/hicolor/24x24/apps/steam.png
/usr/share/icons/hicolor/256x256/apps/steam.png
/usr/share/icons/hicolor/32x32/apps/steam.png
/usr/share/icons/hicolor/48x48/apps/steam.png
/usr/share/man/man6/steam.6.gz
/usr/share/pixmaps/steam.png
/usr/share/pixmaps/steam_tray_mono.png
/usr/share/ubuntu-mate-welcome/img/applications/steam.png
/var/lib/apt/lists/repo.steamstatic.com_steam_dists_precise_InRelease
/var/lib/apt/lists/repo.steamstatic.com_steam_dists_precise_steam_binary-amd64_Packages
/var/lib/apt/lists/repo.steamstatic.com_steam_dists_precise_steam_binary-i386_Packages
/var/lib/dpkg/info/steam-launcher.conffiles
/var/lib/dpkg/info/steam-launcher.list
/var/lib/dpkg/info/steam-launcher.md5sums
/var/lib/dpkg/info/steam-launcher.postinst
/var/lib/update-notifier/user.d/steam-install-notify
I assume leftovers from upgrades. Do see any issues with with me manually removing them?