gistfile1.js

files.items
.filter(function (file) {
  // search parents array looking for atleast once
  // parent that has the id you are looking for
  return file.parents.some(function (parent) {
    return PARENT_ID_YOU_CARE_ABOUT == parent.id
  });
})
.forEach(function (file) {
  // do stuff with each file after filtering here...
});