Sorry, but I'll take Webster's word when it comes to words.
Never quote or link me educational resources when trying to state a rebuttal, it just makes me try harder to educate the masses properly. =D
You should know that Merriam-Webster is one person picking what they think the definition should be and 3 people agreeing with them after they spend a couple hours trying to figure out how it's used, and Webster's first dictionary basically just ripped off the Oxford English Dictionary, changed the spellings of thousands of words and omitted words he didn't care to have taught in American classrooms. I challenge you to dispute it.
However as I stated in my very first sentence, anime is only a partial word, not a style as you think it means. Japanese write the English term "animation" in katakana as アニメーション (animēshon), and the term アニメ (anime) (notice the first three characters are the exact same) emerged in the 1970s as an abbreviation. So using the term anime, you're just using the shortened version of the word animation, where once again, as I said before, the industry, meaning all companies who produce animated works worldwide, refer to any animated material as animation, or anime if they are using the shortened form. They are all one in the same thing. Grab an encyclopedia made after the 70's and look it up.
The 'style' of animation referred to by Webster is indeed the style of animation made popular by Japanese artists over the past 70 years, but no single animation artist in Japan will agree with Webster's definition because they themselves classify all animated works as anime, not just their own. Personally, I'll take their word over Webster's for it's use since they created it, not Webster. The use of the word to describe Japanese cartoon's style is purely an American created use, and a poor one at that. It's like saying can't or RSVP instead of spelling it all out as cannot or reply please and then saying it means the color green. And people wonder why the US educational system is a failure when compared to most other developed nations...
Learning is fun isn't it? 
@GoaFan77 - I meant the term 'American anime' is coined and used in Asian countries not the term anime itself. The term anime is the Japanese shortened version of the word animation as I described above, and to them all animation is anime is animation. Cartoons are just cartoons if you want to compare all of the ones you've watched. Bison is possibly, like many people from the US, applying the word incorrectly.