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I don't understand, the update message only activates when you open GOG Galaxy, but it will only update if Galaxy is not already running....? Quite a contradiction, unless I'm missing something.
What's not to get?

Galaxy starts, checks for updates, notifies you of the update and gives you the choice to either restart and update immediately or to keep doing what you're doing and complete the update the next time you start Galaxy.
With me a pop up window came up when the update was available.
Like other said just launch it and wait for the popup to appear.

A "check for updates" option would be nice though.