No, アニメ is literally short for アニメーション. "Anime" is a loanword derived from アニメ with a different meaning than アニメ because it doesn't make sense to borrow a word

No, アニメ is literally short for アニメーション. "Anime" is a loanword derived from アニメ with a different meaning than アニメ because it doesn't make sense to borrow a word for "animation" since there already exists one.