Yet, if all goes well, Greig's epic tale of three generations of a Highland community might just have matured into something even more significant.
Originally produced by the Royal Shakespeare Company in 2000, and now receiving its Scottish premiere at Dundee Rep, Victoria takes place over three time zones - 1936, 1976 and 1996. A large ensemble of actors play some 32 characters, at the centre of which are three very different women, all called Victoria.
"It's very strange going back to the play after all this time," says Greig, "but it's also very interesting. There's an extent to it being like meeting one's younger self, and on one level that writer was very gauche and very different to the writer I am now. But it's also fascinating to see the level of ambition that writer had then. I didn't realise, but there are lines in Victoria that reappear in [Greig's recent Edinburgh Festival Fringe play] The Events, so it's interesting to see some of the themes that run through my work. So, while it's not without its awkwardness, Victoria is a play I think still stands up."
Originally conceived as a trilogy of three separate plays that even the RSC's resources were unable to cope with, the inspirations for Victoria were many.
"I was very interested in the Spanish Civil war," Greig remembers, "and at the time the war was going on in Bosnia. In essence, it was in defence of the idea of multi-culturalism and Europe living together, and it seemed all these ideas were going to the dogs. The phrase "ethnic cleansing" came out of the war in Bosnia, which we'd never heard before, and Europe was a very fragile place.
"So I was looking around, and I thought of all these young men going out to take part in the Spanish Civil war and fight for something they believed in. It was their choice to go out there, and I suppose I asked myself why this didn't happen now.
"To put it crudely, why wasn't there an International Brigade going out to defend Bosnian Muslims, and what was it about the 1930s that made cause and possibility so inspiring?
"At that time in 1996 as well, it felt very much like cause and belief had gone. One of the interesting things is that the play has developed an invisible fourth act, following the three acts set in 1936, 1976 and 1996. When it was first staged, 1996 was essentially the present day.
Now 15 years or so on, we've had 13 years of a Labour Government, we've had devolution, we've had Iraq and we've had the coalition. The whole world has changed so much, so now, when we see Victoria at the end of the play, we now know what's going to happen to her."
One of the major devices in the play is having the cast play different characters in each act, with all three Victorias played by the same actress.
"Theatrically speaking, I was interested in the effect of that," Greig says. "It's like music, in that you can play the same chord, but it will have different resonances depending on what else is around it.
"With the Victorias, I wanted that feeling of young female energy, and each of them kind of becomes the spirit of their age."
At the time Victoria was commissioned, Greig was one of the rising stars of his generation, with his first full-length professional plays, Europe in 1994 and The Architect ion 1996, being produced by The Traverse Theatre. The artistic director of Scotland's new writing theatre at the time was Philip Howard, who directed both plays. With Howard having recently been appointed artistic director of Dundee Rep, his new production of Victoria not only marks his directorial debut at his new artistic home. It also reunites him with Greig for the first time since the Traverse days, when Howard also directed Greig's plays, Outlying Islands, The Speculator and Damascus.
"I've always wanted Victoria to be seen in Scotland," says Greig, "but I wanted to hold out for a really special production and, when Philip approached me, because I've collaborated with him so often, it felt right. I think he's done a lovely job, and I think he really understands my writing."
For Greig, 2013 has been quite a year. His stage version of Roald Dahl's Charlie and the Chocolate Factory has become a West End hit, while his Edinburgh Festival Fringe play, The Events, was similarly acclaimed. Opening hot on the heels of Victoria is the National Theatre of Scotland's revival of Dunsinane, Greig's sequel of sorts to Shakespeare's Macbeth.
This summer also saw the publication of The Suspect Culture Book, an archive of Suspect Culture, the theatre company Greig formed with director Graham Eatough while they were both at Bristol University. As well as a series of essays about the company, the book contains Greig's scripts for three of the company's most important works; Timeless, Mainstream and Lament.
While Greig remains as prolific as ever, he might just be about to disappear from public view for a while. "I have a pile of writing to do," he says, "so there won't be a new play by me onstage for at least another year now. "
Victoria, Dundee Rep, September 4-21.