The style of animation in Legend of Korra is a tribute to asian culture, like the series itself. It's also animated in Korea which probably adds to the overall feeling.
All American animation since the 1990s are outsourced to Korea, so in conclusion, ALL AMERICAN CARTOONS SINCE 1990s ARE ANIME :p
Anyway, anime is short for animation. Japanese people are lazy that they wouldn't want to pronounce a whole word or phrase if they think it's too loong. A good example is 'pasokon' for 'personal computer' or 'PC'.
When Americans started to promote PCs they used the whole phrase and not the short form of 'PC' that we know of today. Because Japanese always needs vowels after a consonant, 'PC' just wouldn't fly and the Japanese were to busy working overtime in their overpaid job to buy overpriced goods that they had no time to pronounce the whole phrase over the cubicles. And thus, they invented the word 'pasokon' and then Americans invented 'PC' and the Japanese are still kicking themselves for inventing a longer short form for PCs.
The same deal goes for anime. Although in this case it was invented because "TVアニメーション" just isn't marketable and asking mangaka to stylize the "ション" would increase the overhead budget. So thanks to the accountants and the marketing department, "アニメ" was born.
And yes, basically 'anime' and 'animation' are the same thing in Japan. So, every animation made anywhere in the world is colloquially called an 'anime' in Japan. If anything, it's THEM that are too weeaburgery to use their own word for animation, "動画".