You are right, that particular article alone doesn't spell it out completely. But other articles from this author do: https://archive.strongtowns.org/journal/2022/6/15/a-parallel...

The cited article alone simply admits that upzoning won't result in cheaper housing. Because the market is broken (and only socialized housing can fix it), but we must do upzoning anyway.

That article also doesn't support your assertion. For example, they specifically call out parking minimums and minimum lot sizes (both density-lowering regulations) as major drivers of high housing costs.