1) The "distributed ownership" bit – purchase shares representing fractional ownership of something.
2) The "collaborative price finding" bit – use liquidity and misc market forces to find the market price of most things in a fast, continuous, and least painful way.
You're talking about 1, which yes, totally irrelevant. They're talking about 2, which is very relevant.
I'll concede that if you want to be pedantic about semantics, "market" is better than "stock market", but would counter that people think of a "market" as a place where you go to buy lettuce, rather than a conceptual price-finding environment. The stock market concept better matches this abstraction in laypeople's minds.
In even more obvious cosmetic comparisons, the word "Stock" is in embedded in the company name "StockX", and when you go to the "stockx.com" url, there's a ticker of live shoe prices scrolling sideways similar to the traditional stock market displays. The landing webpage also bills itself as, "The Stock Market of Things".
The "stock market" analogy (however flawed it is) is clearly intended to connect to laypeople and not meant to pass a vocabulary test by college econ professors.
Its more like the journalist and developer knows how to make a product relatable. Take notes.
If it's a secondary market like Ebay, say so. That's much more straightforward.
Getting to this point would have required reading past the headline.