The more the ratio favors places, the more human-scale the area tends to be. You can walk, bike, or ride a wheelchair comfortably through much of this space, because there's a new place -- a store, restaurant, house, etc. -- every few yards and there are fewer serious barriers such as highways or big parking lots. If there are also shade trees, benches, wide mixed-use paths, and other human-friendly features then it becomes even more accessible for even more people.
The more the ratio favors non-places, the less human-scale the area tends to be. It's designed for cars. That means if you can't or don't want to drive, you are screwed. Getting around without a car is difficult, dangerous, illegal, or downright impossible. And cars are risky even for passengers, given the number of collision deaths. Devoting some space to high-speed travel makes sense, but the more you do that, the less you have for everything else, which quickly becomes a problem.
I will quibble about their definition of greenspace, though. It doesn't mean just empty lots and medians. It means ALL the plant-covered parts of an urbanscape. That matters for a variety of reasons, most of which can be condensed into: 1) Wildlife needs greenspace to survive, the more the better. 2) Humans need greenspace to stay sane, the more the better. Defining non-park greenspace as a non-place ignores both of these vital services that it provides. Seriously, those stupid lollipop trees in the median keep the sun from baking pavement and pedestrians, provide habitat for birds, and discourage people from murdering each other. A borrow pit become a runoff pond is a layover for migrating waterfowl. If you add fish, verge plants, a few willows, etc. then it's a parklet. You can even add a dock for boating/fishing and a picnic table to make it more appealing. But it's the water that makes it a crucial resource in town where little surface water remains to support wildlife.