Then you are wanting to run an oauth server. However, you will also need to provide library functions to allow third party apps to use your service (or they won’t). So, basically you need both.
Oauth uses standard HTTP requests, so you don’t need to use Meteor to write an oauth server - there are a number of “other-language” options out there. If you’re going to roll your own (or fork an existing one) you’ll need to do your due diligence regarding security (authentication quality, vulnerabilities, etc).