(Note: I am using the term "New World" loosely to apply to the areas of Greenland, Iceland, and the Americas since it seems like an apt term to use as a non-historian.)
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What compelled the Vikings to:
Despite the fact that:
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Here is my attempt at trying to personally rationalize this:
My first assumption is that countries/states/nations essentially see exploration and settlements as an investment and would assess if it were a good or bad investment before performing them. My second assumption is that crossing the Atlantic must be unbelievably expensive if no other country, in 500 years, would even bother thinking about exploring the Atlantic (And for a completely different economic reason.)
If both of these assumptions are vaguely correct, then it would appear that the Vikings, if being remotely economically practical or utilitarian, should not have cared about the New World at all.
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TL;DR:
While much more can always be said on these topics, I summarized the current academic consensus on the Norse expansion into "the New World" and its apparently failure (or discontinuation) before in:
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What did the Vikings see in the new lands beyond the Atlantic?
In short, Exotic animal products "for the market in Europe.", such as walrus tusk.
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Why did no other country see the same vision for ~500-600 more years?
At that time (around 1000 CE), no other European people except for the Norse people had a stable ocean-going ship and nautical technology like the viking ship, and even their voyage presupposed that to call at ports in the North Atlantic Isles like Iceland and Greenland where the Norsemen had settled in. In other words, it was almost impossible even for the Norse people to conduct a non-stop direct voyage from Europe to "the New World (possibly except for Greenland)", and neither did other group of peoples in Europe have much incentive to plan such a kind of voyage (The Norse people had already played a role of middlemen for the exotic arctic products from the arctic circle that they traded with hunter-gatherer there during the Viking Age).
Carracks and caravel types of ships that the Portuguese and the Spanish people employed, with the combination of different type of sails (triangular lateen and square) for better adaptability to the direction of wind was primarily the invention of Later Middle Ages, and very roughly speaking, developed on also the combined foundation of shipbuilding traditions both in the Mediterraneans and in the Northern Seas (North Sea and Baltic).
It was not until about the end of the 13th century that the confluence of two medieval maritime worlds in the North and in the South, and we have to wait further later for the interaction of shipbuilding technology.
As for more details of the historical development of shipbuilding up to the end of the Middle Ages, you can check some of the posts by /u/terminus-trantor: