Welcome to the community, Alexis! :grinning_face_with_big_eyes: Printing occurs at the application level, meaning that you can print from your browser app or the standalone Airtable app. However, Zapier and Integromat access things at the data level, so they have no way of printing anything.
Depending on your operating system, there may still be a way to automate what you want using system-level automation software. This type of software records mouse movements, keystrokes, etc., and can recreate them when told to do so. On the Mac, the built-in Automator tool is one such program, though it has its limitations. Still, it could probably be set up to open Safari to a specific URL like a shared Airtable view, then print that view. There are likely similar programs for Windows, though I don’t know any names off the top of my head.