Is Payment requests API built to work as part of PWA only, or can be used in regular web sites as well?
A website becomes a PWA when it uses the PWA APIs. There's no strict technical definition of what a PWA is. It's fair to assume your website needs three things to qualify for being a PWA: you need to be running under HTTPS, you need a Web App Manifest and you need a Service Worker. The Payment requests API requires HTTPS, but that's the only matching requirement here.
So basically: no, you don't need to have a PWA to use the Payment requests API, but your website will become more PWA-like when you use it.