How to download Google Slides as images?

The following worked for me:

Set up

Under Resources > Developer Console Project > View Developers Console, enable both the Slides API and the Drive API.

Execution

Replace the ID taken from the Slides URL in the start() function, and run it, e.g.:

https://docs.google.com/presentation/d/<id>/edit

and the function will save the PNGs to your Drive. This could be extended to group them all in a specific folder etc.

function downloadPresentation(id) {
  var slideIds = getSlideIds(id); 

  for (var i = 0, slideId; slideId = slideIds[i]; i++) {
    downloadSlide('Slide ' + (i + 1), id, slideId);
  }
}

function downloadSlide(name, presentationId, slideId) {
  var url="https://docs.google.com/presentation/d/" + presentationId +
    '/export/png?id=' + presentationId + '&pageid=' + slideId; 
  var options = {
    headers: {
      Authorization: 'Bearer ' + ScriptApp.getOAuthToken()
    }
  };
  var response = UrlFetchApp.fetch(url, options);
  var image = response.getAs(MimeType.PNG);
  image.setName(name);
  DriveApp.createFile(image);
}

function getSlideIds(presentationId) {
  var url="https://slides.googleapis.com/v1/presentations/" + presentationId;
  var options = {
    headers: {
      Authorization: 'Bearer ' + ScriptApp.getOAuthToken()
    }
  };
  var response = UrlFetchApp.fetch(url, options);

  var slideData = JSON.parse(response);
  return slideData.slides.map(function(slide) {
    return slide.objectId;
  });
}

function start() {
  downloadPresentation('Slides document id')
}