The two great rivals meet at the Stade de France on Saturday — 28 years after their previous meeting in a final.
That resulted in a memorable South Africa victory — 15-12 after extra-time with all their points scored by Joel Stransky — and the iconic image of black president Nelson Mandela presenting the trophy to the Springboks' white captain Francois Pienaar.
Stick said the wins by a single point in the quarter-final and semi-final in the tournament in France had meant a lot.
"The way we fought the last two games, it was about bigger than the game," said Stick on the eve of the game.
"Hopefully we will keep on fighting and make sure we give our people back home a bit of light."
Stick spoke of the immense impact that the South Africa win in 1995 had on the image of a sport which at the time was seen as almost the last bastion of apartheid.
"When I think about that last final, I was an 11-year-old back then, that 1995 game really changed the image of the game back in South Africa," he said.
"Every kid just wanted to be Joel Stransky — I was called 'Township Stransky' — or James Small and these guys.
"We always go onto the streets and sing and celebrate. Whenever I think about that moment, it always feels like yesterday.
"The legacy those guys — Joel Stransky, Francois Pienaar — left made it possible for us to be where we are at the moment."
'A fairytale story'
Stick said he hoped many black players would follow the path of current skipper Siya Kolisi, the first black Test captain of the Springboks.
The team's thrilling 29-28 win over hosts France followed by the 16-15 victory over England in the semi-finals has energised a country which has high unemployment, is still torn by deep societal divides and is struggling with poverty.
"You ask about our background... to be honest this is what we live for, it's about the people who are dreaming to be in our position in the communities back in South Africa," he said.
"We just want to do everything in our power to make sure we are reuniting those people.
"For a guy like Siya (Kolisi), coming from where he did… wow, no doubt in 20 years, there will be a lot of Siya Kolisis, boys who have got here irrespective of background.
"It is like a fairytale story when you talk about Siya, but it surely does change people’s lives, whatever their background, if you have your head in the right place, if you have a goal and keep chasing it."
Stick said despite the current team being on the older side, this was the World Cup they had been aiming for when Rassie Erasmus and Jacques Nienaber took over a shambolic team in 2017 — and the World Cup win two years later had been an unexpected bonus.
"It was never a secret, if you look back from 2018 our focus was always on 2023," he said.
"A miracle happened in Japan but it was always part of the plan to make sure we performed at our peak in this World Cup."
Both South Africa and New Zealand lost once on their way to the final — the former to Ireland and the latter to France — although the Springboks are arguably more battle-hardened.
They played the Scots and Irish in the pool stage before narrow wins over France and England. In contrast, the All Blacks, aside from the opening defeat against the French, were only tested by the Irish in an epic quarter-final.
"The All Blacks have won the World Cup three times, we have won it three times, so this game is almost bigger than just a World Cup final," said Stick.
"Whoever wins is going to have bragging rights for the next four years."