The Georgia international, who arrived from Dinamo Batumi in July, has played an instrumental role in Napoli's impressive start to the season, with Luciano Spalletti's side eight points clear at the Serie A summit.
No player has been directly involved in more goals this term than Kvaratskhelia (11 - scored six, assisted five), with his tally only matched by team-mate Victor Osimhen, who is the leading marksman in the Italian top flight (nine).
Unbeaten after 15 games, Napoli's surge has been all the more impressive considering three key players left in the close season, with Kalidou Koulibaly joining Chelsea and all-time top scorer Dries Mertens and Lorenzo Insigne departing on free transfers.
But Hamsik - the club's record appearance maker (520) - is delighted at how the likes of Kvaratskhelia and Osimhen have stepped up to the plate, along with defender Kim Min-jae.
"Kvara has incredible dribbling ease and he is among the best in the world," the 35-year-old said.
"It's incredible to see this Napoli team without the three most important players.
"Everyone needs symbols, someone to represent the club. For the fans, it was a shame [when those players left].
"But I must say it's good how Napoli took players who play great, getting good results like Kim, Kvara, Osi, and also reduced the wage bill."
Now plying his trade with Turkish side Trabzonspor, Hamsik spent 12 seasons at Napoli and became the club's all-time leading scorer with 121 goals, though he has since been surpassed by Mertens (148) and Insigne (122).
The former Slovakia captain revealed he declined several offers to move away from Naples, but has no regrets over those decisions.
"There were teams that wanted me," he added. "The first was Milan with [Massimiliano] Allegri in 2012, then [Walter] Mazzarri at Inter.
"There was Juve - there were a few calls with [Pavel] Nedved, but I never thought about it.
"I never needed to change. I was happy and renewed five times in 12 years, which is quite a number. The club gave me what I wanted, I was happy, my family too, and the fans loved me more and more."