I don't think it's accurate to say that it has no intrinsic value by definition. If you do a fundamental analysis on the options without reference to their market value, the Black Scholes formula will tell you that an option, even an option out of the money, is worth something. That is the definition of intrinsic value.
Options out of the money also clearly have a market value, for public companies at least.
According to the first sentence in the article you link, "Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, using fundamental analysis." That's precisely what I am talking about.
Options out of the money also clearly have a market value, for public companies at least.