Your while loops are constantly blocking the thread, so your callback function can't run.

Instead of the while loops, you can use an interval:

var bby = require('bestbuy')('<Actual BestBuy Api key in original code>');

function check() {
  console.log("HERE");
  bby.products(6465789,{show:'sku,name,salePrice,onlineAvailability,inStorePickup,onlineAvailabilityUpdateDate'}).then(function(data){
    console.log(data);

    if (data['onlineAvailability'] == false)
    {
      clearInterval(loop);
      console.log("In Stock");
    }
  });
}

const loop = setInterval(check, 3000);

Even cleaner may be using async/await to wait 3 seconds after receiving each response:

var bby = require('bestbuy')('<Actual BestBuy Api key in original code>');

const wait = require('util').promisify(setTimeout);

async function check() {
  console.log("HERE");

  const data = await bby.products(6465789,{show:'sku,name,salePrice,onlineAvailability,inStorePickup,onlineAvailabilityUpdateDate'});
  console.log(data);

  if (data['onlineAvailability'] == false)
  {
    console.log("In Stock");
    return;
  }

  await wait(3000);
}

check();

There are several points to improve your code:

• Use setInterval to execute code in regular interval, instead of using spin lock in a while loop
• Use async/await to improve readability
• Instead of checking condition == false, simply check !condition
• Instead of doing if(!condition){x = false}, simply do x = !condition
• Use dot notation instead of bracket notation to access object property if the property name is not variable. This can take advantage of intellisense of IDE if the object shape is properly documented and reduce typo.

const t = setInterval(async () =>{
    const data = await bby.products(6465789, { show: 'sku,name,salePrice,onlineAvailability,inStorePickup,onlineAvailabilityUpdateDate' });
    console.log(data);
    isSoldOut = !data.onlineAvailability;
    console.log(isSoldOut);
    if(isSoldOut)
    {
        clearInterval(t);
    }
},3000);