Right, but see the details for estimated range and the map. Not that India has any foreseeable need to nuke Argentina but it's not in range. It's entirely possible the public data is wrong and the Agni VI has a global range.
But by definition if you can put something into a 350x350 km low earth orbit (something like 7800m/s total delta V) you could also deliver a re-entering payload from your launch site to any other spot on earth, within the limitations of the inclination you're launching to.
I was under the impression long range missiles aren't much use in global warfare anymore, because they are easy targets for missile defence systems.
Even if your target doesn't have missile defence systems, any ally of theirs along the route can intercept too.
Multiple sources think that the real range is an ICBM level. And the Indian government purposely limits it's range. No strategic reason to communicate a larger range than needed and why have an headline that reads, "India develops capability to nuke Europe or US"?