Your counterargument is that they didn't have a problem in 1980, when they had less people and the same amount of land. I can't disagree with that, but it isn't relevant.
> Many, many other countries don't have a lot of natural resources and are not having these problems.
They have the 3rd largest economy in the world. It goes US, China and then Japan. 30% higher GDP than the next contender, Germany. If there are any non-linear economic effects at all between size and labour market, Japan is going to find them first.
And the chart in that article shows that they basically stopped having children in 1980 which would be consistent with a "running out of resources" hypothesis as a root cause. If they hit a wall in economic carrying capacity circa 1980 that chart would supporting evidence.