Well navigation.vm is responsible for generating the same <ul><li /></ul> tags that are used in the html you uploaded.
I'm betting that all you'd need to do is tweak the existing navigation.css in the theme to support the multi-column layout...
The problem, from the Liferay side, is not just the navigation.vm and the navigation.css, there's also javascript invoked to set up and manage the Liferay navigation stuff. I'm not sure what would happen if you tried gutting portions of navigation.vm / navigation.css without also touching the javascript...
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