There are applications besides web browsers that require passwords. For example, password-protected documents, or encrypted archives. A password managers that requires, or only supports, web browsers is incomplete.
A password manager that is only usable in a web browser may be annoying to use for non-web-related tasks, but presumably you can just switch to your web browser, open up the password manager, and then search for what you need within it. It's not like the password manager is restricted to only giving you access to the passwords for the current site.
Regardless, 1password X does not provide the full functionality of the native apps, so it's fair to say a Mac or Windows app is required for full functionality anyway.
