It looks like he’s first using tesseract to recognize his handwriting and convert it into text. Tesseract doesn’t do a perfect job so the recognized text is full of mistakes. He treats the mistakes as spelling mistakes and “asks” GPT-3 to correct them. This is a very clever idea and will greatly improve current OCR efforts.
I think from his explanation in the article it's quite straightforward to implement it yourself: get a GPT-3 subscription at OpenAI or MS Azure, use the API as described in the article, voilà.