The Motorola Connect app isn't required to get use out of your Moto 360, but it is if you want to customize any of those watchfaces that come pre-installed on the device. The latest update doesn't remove that restriction, but it does allow you to hop straight to the tweaking stage from the Android Wear app directly. Take a look.
Left: old, Right: new.
As you can see in the shots above, an entry titled "Settings" has appeared in the menu between "Set on watch" and "Hide on watch."
Clicking this option shoots you out to the same customization page you would go to by navigating through Motorola Connect directly, so it does little more than give you a choice in how you get there.