No, it does not.  The "world's third oldest airline" refers to an airline that is still operating today.  Have a look at the table again.  Qantas is thirded by KLM and Avianca.  However, according to the reference that is actually cited, Qantas claimed that they are the world's second oldest airline. http://www.qantas.com.au/infodetail/about/FactFiles.pdf