That article talks about privatization of "Fair Park", not "The State Fair of Texas". It's a little deceptive because at the end it mentions "home of the state fair". The Stare Fair of Texas is a private non profit organization. To my knowledge, it's never been owned by a government entity.
The State Fair of Texas is a Texas nonprofit organization granted tax-exempt status by the Internal Revenue Service under Section 501(c)(3) of the Internal Revenue Code.
The Fair does not receive any government funding or support. Its nonprofit purpose is funded through the proceeds from the annual State Fair of Texas event.
http://bigtex.com/about/financialhighlights/
But of course, as you said, it's a moot point since they lease the land from the city, but the city still owns the land.