Word Ladder JavaScript Implementation
Naming

I suggest renaming getShortestPathBetweenWords() to  findShortestLadderDistance() for the following reasons:


get is recommended as a prefix for simple lookup functions. Use another verb such as compute or find for meatier, computationally heavier functions. 
You are actually computing the distance of the shortest path, not the path itself. And a ladder is a more specific word for path whose neighboring words differ by exactly one substitution.


Further naming suggestions:


Rename _generateNewWords() to generateNeighbors()
Rename level to distance
Rename st to start
Rename newWord to next
Rename q to queue
Rename listOfWords to neighbors
Rename charArray to chars


Style

Instead of while (queue.length !== 0) I suggest the more self-documenting while (queue.length &gt; 0) as the length can never be negative.

Also, don't needlessly mix "" vs. '' for strings.

Specification

Right now you are returning a distance of 0 when there is no path and a distance of 1 if start equals end. I suggest following the common definition of path length and return Infinity and 0 instead.

You might also want to pass the alphabet as a parameter instead of having a hard-coded 'magic' constant in your _generateNewWords() function. It can easily be computed from your dictionary as alphabet = [...new Set(dict.join(""))].

Also, you currently allow any word for start while end must be part of the dictionary. I recommend allowing non-dictionary words in both cases for consistency.

Performance

Your main performance bottleneck is the checkinDictionary() function. If you keep track of a set of open words which you haven't visited yet, you can replace that function call with a simple open.has(word). Set lookup time is constant and thus much faster than iterating the whole dict array.

You then have to pass the open set to generateNeighbors(). The isVisited map is no longer needed.

Another performance drain is performing string splitting via let charArray = word.split('') in the inner loop of _generateNewWords. You can push that to the outer loop.

Also, you currently treat start.length &lt; end.length as a special 'shortcut' case. You could generalize this to start.length != end.length.

Sample code

Applying all those modifications to your code yields: 



function findShortestLadderDistance(start, end, alphabet, dict) {
  if (start === end) return 0;
  if (start.length != end.length) return Infinity;

  let queue = [start];
  let distance = 1;
  let open = new Set(dict);
  open.delete(start);
  open.add(end);
  
  while (queue.length &gt; 0) {
    for (let i = 0, length = queue.length; i &lt; length; i++) {
      let next = queue.shift();
      
      for (let neighbor of generateNeighbors(next, alphabet, open)) {
        if (neighbor === end) return distance;
        
        queue.push(neighbor);
        open.delete(neighbor);
      }
    }
    distance++;
  }
  return Infinity;
}

function* generateNeighbors(word, alphabet, open) {
  let chars = word.split("");
  
  for (let i = 0; i &lt; chars.length; i++) {
    let char = chars[i];
    
    for (let j = 0; j &lt; alphabet.length; j++) {
      chars[i] = alphabet[j];
      neighbor = chars.join("");
      if (open.has(neighbor)) yield neighbor;
    }
    chars[i] = char;
  }
}

let start = "sand";
let end = "acne";
let dict = 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let alphabet = [...new Set(dict.join(""))];
console.log(findShortestLadderDistance(start, end, alphabet, dict));