Don't be ridiculous. The video narrator specifies that the gold on the basalt must have been present locally at the eruption, but as anyone can tell you who has read the Silmarillion seventeen times and memorized every single historical fact therein (while being unable to, for example, name their legislative representatives), Mount Doom is canonically in New Zealand, thus the gold in Iceland can't be from the One Ring. I give this post a 1/10, it would be a 0/10 but Jeff Bezos is censoring me.
I mean, while we're waltzing around the absurd, how meaningful do you really think the continents remain at magmatic depths? We're literally talking about the space where the bedrock melts and flows in the unknowable oceans of Sauron's marmalade, after all. I think the ring spent eons swishing around before reassembling like a blended up sea sponge before making its way back to the surface in the modern-day land of the elves (Iceland). It's only a matter of time before the trolls in the forests of Norway begin amassing their forces. As for that video's narrator, I think his name is Dave Sméagol, so I'd take his misdirections with a pinch of salt.
As a non-geologist, it seems plausible to me that gold that was somehow subsumed into the mantle in New Zealand could migrate to Iceland in the span of thousands of years. As Sméagol pointed out, though, gold coming up in the magma would be more diffuse and not create an identifiable layer on the surface of the lava rock. You're right, though, he's hardly a reliable narrator when it comes to His Precious, so that could be a misdirect. And perhaps there's some attribute of magically endowed gold that causes it to behave in unexpected ways. I searched Google Scholar, but couldn't find any peer-reviewed studies on the physical properties of magic rings.
Antipode of Iceland is not too far (relatively speaking) from New Zealand. Going the other way around it's really Spain, so if The Ring was slowly traveling through Earth's core, one could imagine that it made "wrong turn at Albuquerque" and instead surfacing in Spain it hit Iceland. QED