I've already built a Shopify app that can do this. You just download a small multi-platform app (windows/mac/linux) that runs in the background. When new orders come in, about 5 seconds later they print automatically to the printer I have set to the default.
I have no idea if shopify has any blanket policy about eligibility for apps that need you to download anything, but as long as that's not the case it will be on the app store fairly soon. Just waiting for a response from the apps team on if I can submit it to the app store or not.
