Yes, this is important, too (see [email protected]). But no-lawns doesn't reduce car traffic, neither does it single-handedly create more walkable and public-transport-friendly communities. But you're right to notice that OP's meme doesn't make a compelling argument in itself.
There are limits to how many trees, how big they can be and how close to the house you can have them. There is also a ton of car infrastructure that needs to be spread out across all the houses that takes up a good percent of the land no matter how you slice it
The most important difference though is that each person only has access to their stamp of nature that is 1% of the island. With the apartment all 100 people living there have access to 96% of the nature on the island.
It doesn't have to be just nature either. You can use it to build playgrounds, outdoor gyms, running tracks, community centers and tons of other public use things.
I hate apartments, I believe humans should spread out and live in lower densities. Cities are important in our current infrastructure and a necessary evil.
I've moved away from a city and been living in a small town past 2 years and cars are more important here than ever which is just shifted me from one evil to the next. Public transport becomes less relevant the more remote you go.
Wonder if there's a perfect balance between pollution and nature. I'm in the mountains so bikes aren't the most comfortable either and useless in case of emergency with an elderly.