由于allWords = arrPush(allWords, words[word]);和arrPush的编写方式，您的代码失败。
第一次调用arrPush时，传递一个空数组allWords和要推送到该数组的字（第二个参数）。
但是因为函数arrPush没有返回，你基本上是在取消设置allWords，也就是allWords = undefined，所以代码错误是因为没有undefined的length属性。
解决这个问题的关键是，只需将return allWords;作为arrPush函数的结果，以便allWords不断设置为数组的最新（稍微更完整）版本。

function deleteTheLongestWord(str){
  
    let arrSent = strSplit(str, ".");
  
    let allWords = [];

    let biggestWord = '';

    for (const elem in arrSent) {
        let words = strSplit(arrSent[elem], ' ');
        for (const word in words) {
          if (words[word] !== ''){
             allWords = arrPush(allWords, words[word]);
          }
        }
    }
  
    for (const i in allWords) {
        if(biggestWord.length < allWords[i].length){
            biggestWord = allWords[i];
        }
    }

    allWords = allWords.filter(function(e){
        return e.length === biggestWord.length
    })
    for (let i = 0; i < allWords.length; i++) {
        str = str.replace(" " + allWords[i], '');
    }
    console.log(str);
}

function arrPush(allWords, word){
  allWords[allWords.length] = word;
  return allWords;
}

function strSplit(str, delimiter){
    const arr = [""];
    const len = delimiter.length;
    let idx = 0;
    for (let i = 0; i < str.length; i++) {
      let sample = "";
      for (let x = i; x < i + len; x++) {
        sample += str[x];
      }
      if (sample === delimiter) {
        i += len;      
        idx += 1;      
        arr[idx] = ""; 
      }
      if (str[i]) arr[idx] += str[i];
    }
    return arr
}

deleteTheLongestWord('word wooord wooooooooord wooooooord. wooooooooord woooooord woooord wooooooooord');

下面是一个简短的函数，它完成了预期的任务：删除字符串中所有最长的单词。

const testString =
  "word wooord wooooooooord wooooooord. wooooooooord woooooord woooord wooooooooord";
const expectedResult = "word wooord wooooooord. woooooord woooord";

function deleteTheLongestWord(string) {
  const words = string.split(" ");
  const max = Math.max(...words.map((word) => word.length));
  return words.filter((word) => word.length < max).join(" ");
}

const result = deleteTheLongestWord(testString);
console.log(result);
console.log(result === expectedResult);

这里是同一个函数，但有更多行注解和控制台日志，因此可以理解这个过程。

const testString =
  "word wooord wooooooooord wooooooord. wooooooooord woooooord woooord wooooooooord";
const expectedResult = "word wooord wooooooord. woooooord woooord";

function deleteTheLongestWord(string) {
  // Get all words in an array
  const words = string.split(" ");
  console.log(words);

  // Create an array containing the length of each words
  const wordsLength = words.map((word) => word.length);
  console.log(wordsLength);

  // Find what the maximum length is
  const max = Math.max(...wordsLength);
  console.log(max);

  // filter the words array keeping only words that are less than the max length
  const result = words.filter((word) => word.length < max);
  console.log(result);

  return result.join(" ");
}

const result = deleteTheLongestWord(testString);
console.log(result);
console.log(result === expectedResult);

对于loop方法，可以使用split（），也可以使用filter（）。