I was looking for the same capability. It sounds so simple. Just auto-print my f’n new orders! But nothing was out there.
Some people recommended Zapier and google cloud printing. That’s ridiculously expensive for just print my orders.
After a really long search I finally found the perfect solution. https://www.automatic-email-manager.com/
It’s a small app that runs on a Windows machine. I got all my Shopify orders printing perfectly through my gmail account. The tech support is really fast and responsive.
Can’t say enough good things about this software. And, I can’t believe it’s so hard to find. Hope this helps other e-commerce store owners who want this simple yet important feature.