If a code is written and is working fine in web version, then it will definitely work for mobile version. If you can post your code here, it will be easy to debug.
Also, instead of custom code, you can also use custom validation -> regex.
The regex to check the minimum word limit is (here 100)-
/^\\W*(\\w+\\b\\W*){100,}$/
Source

Thanks Rondev for your response. I will look into regex solution as well.
Here is the code I'm using:
Qualtrics.SurveyEngine.addOnload(function()
{
/*Place your JavaScript here to run when the page loads*/
$('NextButton').hide();
});


Qualtrics.SurveyEngine.addOnReady(function()
{
/*Place your JavaScript here to run when the page is fully displayed*/
var display = $('wordCountDisplay');
    var questionID = this.questionId;
    var textbox =$('QR~' + questionID);
    var that = this;
    function countWords(s){
        s = s.replace(/\\n/g,' '); // newlines to space
        s = s.replace(/(^\\s*)|(\\s*$)/gi,''); // remove spaces from start + end
        s = s.replace(/� ]{2,}/gi,' '); // 2 or more spaces to 1
            if(s == ''){
                return 0; 
            }else{
                return s.split(' ').length; 
            }
    }


    textbox.onkeyup = function(e){
var currWords = countWords(textbox.value)
        display.update(currWords);
        console.log(textbox.value);

if (currWords < 25) {
$('NextButton').hide();
    $('PreviousButton').hide();
}
else {
$('NextButton').show();
}
    }

Use the below code in the JS:
Qualtrics.SurveyEngine.addOnload(function()
{
/*Place your JavaScript here to run when the page loads*/
jQuery('#NextButton').hide();
jQuery('#PreviousButton').hide();
});


Qualtrics.SurveyEngine.addOnReady(function()
{
/*Place your JavaScript here to run when the page is fully displayed*/
jQuery('#NextButton').hide();
var display = jQuery('.wordCountDisplay');
  var questionID = this.questionId;
  var textbox =jQuery(".InputText");


  var that = this;
  function countWords(s){
    s = s.replace(/\\n/g,' '); // newlines to space
    s = s.replace(/(^\\s*)|(\\s*jQuery)/gi,''); // remove spaces from start + end
    s = s.replace(/� ]{2,}/gi,' '); // 2 or more spaces to 1
      if(s == ''){
        return 0; 
      }else{
        return s.split(' ').length; 
      }
  }


  jQuery(".InputText").bind('keyup change',function(e){



var currWords = countWords(textbox.val())
    display.text(currWords);
     

if (currWords < 5) {
jQuery('#NextButton').hide();
   jQuery('#PreviousButton').hide();
}
else {
jQuery('#NextButton').show();
}
  });

});
Also, to show word count, in the question HTML view paste the below code:
 

Thanks Rondev. Interestingly, your code works perfectly for the web version but again it has an issue with the mobile version but this time the opposite! It never shows the next button, even after going above the word limit, on the mobile version.

Next button is not visible in the qualtrics mobile device because we have not typed in the mobile version, if you type in it, you will be able to see the next button.
Also, just to confirm, you can publish the survey and using anonymous link, test it in real mobile device.