Is vermiform appendix no more a vestigial organ?
Short Answer: No, the appendix is still considered a vestigial organ.

Long Answer: The idea that that vermiform appendix is vestigial originated when Kumar et al (1989) removed it from the body, but failed to find any side-effects. From then on, it got widely established that vermiform appendix is a vestigial organ and has lost all its functions during the course of evolution. The reason behind appendix becoming vestigial was given by Darwin himself in The Descent of Man, and Selection in Relation to Sex where he stated that appendix was used by early primates to digest leaves, and slowly became vestigial as ancient humans shifted towards foods like cereals and meat. This theory was also supported by presence of very long cecum in herbivores like koala and horse.

The only problem with this idea was that the role of appendix in only digestion was being considered. As appendix was connected to large intestine, so early scientists (kinda) presumed that it should be related to only digestion.

This theory got its first challenge when Parker et al (2007) suggested the appendix to be a safe-house of healthy bacteria when illness (such as diarrhea) flushes them out of the GI tract. It was based on the understanding, which came in 2000s by Sonnenburg et al (2004) and Everett et al (2004), about how the immune system supports the growth of beneficial intestinal bacteria. This was experimentally established when Dunn et al found that individuals without an appendix were four times more likely to have a recurrence of Clostridium difficile colitis.

After this, more functions of appendix were discovered, especially those related to immune system. It is because of the efforts of Zahid et al (2004) (the one you cite) and Rankin et al (2016) that appendix is now identified to be more related to immune system than digestive system in humans.

Also, research by Laurin et al (2011) and Smith et al (2013) concluded that during the evolutionary course, appendix has evolved about 38 times and lost as many as 6 times, suggesting that the cecal appendix has a selective advantage in many situations and argues strongly against its vestigial nature.

Conclusion: 


Vermiform appendix is identified as Gut Associated Lymphoid Tissue (GALT) and important component in mammalian mucosal immune function, B-cell mediated immune response and extrathymically derived T-cells. 
This structure helps in the proper movement and removal of waste matter in the digestive system, contains lymphatic vessels that regulate pathogens, and lastly, might even produce early defences that prevent deadly diseases.
It is thought that appendix may provide more immune defences from invading pathogens and getting the lymphatic system's B and T cells to fight the viruses and bacteria that infect that portion of the bowel and training them, so that immune responses are targeted and more able to reliably and less dangerously fight off pathogens.


Discussion: The problem is in the definition itself of vestigial organs. The point is that being vestigial is not equal to being useless. See this definition by Wikipedia (emphasis mine):


  In the context of human evolution, human vestigiality involves those traits (such as organs or behaviors) occurring in humans that have lost all or most of their original function through evolution. Although structures called vestigial often appear functionless, a vestigial structure may retain lesser functions or develop minor new ones. In some cases, structures once identified as vestigial simply had an unrecognized function.


Now, since vermiform appendix does not perform its (suggested) original function of digesting cellulose and other indigestible materials, and performs much less of its (possible) function in immune system, it is still officially considered as vestigial organ.

References:
 &bull; Vermiform Appendix - Wikipedia
 &bull; Human Vestigiality - Wikipedia
 &bull; Kumar, Vinay; Robbins, Stanley L.; Cotran, Ramzi S. (1989). Robbins' pathologic basis of disease (4th ed.)
 &bull; Darwin, Charles (1871) "Jim's Jesus". The Descent of Man, and Selection in Relation to Sex
 &bull; Bollinger, R.R.; Barbas, A.S.; Bush, E.L.; Lin, S.S.; Parker, W. (21 December 2007). "Biofilms in the large bowel suggest an apparent function of the human vermiform appendix"
 &bull; Sonnenburg J.L.; Angenent L.T.; Gordon J.I. (June 2004). "Getting a grip on things: how do communities of bacterial symbionts become established in our intestine?"
 &bull; Everett M.L.; Palestrant D.; Miller S.E.; Bollinger R.R.; Parker W. (2004). "Immune exclusion and immune inclusion: a new model of host-bacterial interactions in the gut"
 &bull; Dunn, Rob. "Your Appendix Could Save Your Life"
 &bull; Zahid, Aliya (2004-04-01). "The vermiform appendix: not a useless organ"
 &bull; Rankin, Lucille C.; Girard-Madoux, Mathilde J. H.; Seillet, Cyril; Mielke, Lisa A.; Kerdiles, Yann; Fenis, Aurore; Wieduwild, Elisabeth; Putoczki, Tracy; Mondot, Stanislas (2016-02-01). "Complementarity and redundancy of IL-22-producing innate lymphoid cells"
 &bull; Laurin M.; Everett, M.L.; Parker W. (2011). "The cecal appendix: one more immune component with a function disturbed by post-industrial culture"
 &bull; Smith H. F.; Parker W.; Kotzé, S. H.; Laurin, M. (2013). "Multiple independent appearances of the cecal appendix in mammalian evolution and an investigation of related ecological and anatomical factors"