The op-ed is by a former regional Fed President who doesn't work or speak for the Fed now. However, his argument is that the wealth effect of high asset prices is a key driver of higher spending and rising consumer prices.
Even 10% of people can push the inflation.
It seems that stock market household participation has inched up over the past 4 decades driven by a variety of factors and is likely a (slight) majority participation rate at this point[1][2] although as one might expect heavily skewed towards higher-income households.
[1] https://www.pewresearch.org/fact-tank/2020/03/25/more-than-h...
[2] https://www.usnews.com/news/national-news/articles/2021-03-1...