It absolutely makes sense. All corporations have a market cap because they have shares outstanding and there is a price per share. We can disagree as to whether the share price is what it should be given the lack of trading liquidity, lack of transparency in their books, etc. Nevertheless, there is certainly a share price and a number of outstanding shares.

We can all argue whether Airbnb is worth $2B or $6B and Uber $40+ Billion, but these valuations aren't made up. They follow accounting rules.

One primary example is mark to market. http://en.wikipedia.org/wiki/Mark-to-market_accounting

The key phrase there was"non publicly traded company". By definition, non publicly traded companies don't have (stock) market capitalization, which is the value of all outstanding shares (stock).

last price per share paid (by an investor) times number of shares outstanding?

I don't see why valuation isn't just as good at market cap, if a bit less liquid. same idea.