I have a MacBook air (2016) with OS Sierra. This from @ryanbaer resolved my issue as well, but I next implemented what @rahmanifarid did in his solution (see below in this post). After which I went into Atom clicked the install/restart. It took 3-4 minutes and the Atom restarted on its own with the update installed. So to recap do the following steps:
1) sudo chown -R $(whoami) /Applications/Atom.app/
2) sudo chown -R $(whoami) ~/Library/Caches/com.github.atom.ShipIt/
3) sudo chown -R $(whoami) ~/Library/Application\ Support/com.github.atom.ShipIt/
4) sudo chown (whoami)**:staff /Users/your_user_name/Library/Caches/com.github.atom.ShipIt/***
5) Go into Atom and click restart/install and wait for 5-10 minutes ( if it doesn't come back on its own, check your steps).
6) If it works, volia!
(whoami) = your_user_name = you username on you device that you're using (ex: /User/whoami**/myFolderName/myNextFolderName**
Thanks to everyone including: @rahmanifarid and @ryanbaer for the insight!