I'd say there is within Europe to a degree. Hunting generally is quite traditional in these places, so I guess it's relatively easy to get the 'old world' experience.Why so often, there is a sentiment for "old Africa hunting", and never something like "old Europe style hunting", or "old Australian style hunting", etc ?
Considering game shooting or stalking in the UK. Ponies for extraction, big sporting estates, side by sides, tweed suits, ties, it's all faintly Victorian in many ways. You certainly couldn't turn up to a driven pheasant day in cammo or with a semi-auto. No tie or an over under is pushing your luck in many places!
Then there's the driven hunting traditions of continental Europe, Germany especially. Jagdhorns, outfits, all the ceremonial, rituals of respect for the quarry etc etc. Again, outwardly very traditional at least, although in reality a lot of modern hunting culture, horn calls and ceremonial was actually developed and formailsed by either the Nazis in the 30's (West) or by the Soviets in the '50's (East).
As for other countries, well old India appeals, but perhaps the rest of the world diesn't have that rigid tradition of closely defined methods, tools and techniques, or such a wealth of documented hunts by 'names'. It's more a tradition of subsistence hunting by the common man, which, whilst a strong cultural heritage, might result in less nostalgia overall, especially as it's much more free to change and evolve by time or region.
I'd still be up for a free range US buffalo hunt with a black powder 45-120 mind!