Domain registrars have had application programming interfaces for a long time. Extensible Provisioning Protocol (EPP), the machine-to-machine language registrars use to talk to registries, reached Proposed Standard status in March 2004 — more than two decades ago. Every ICANN-accredited registrar built on top of it since has had some form of REST or SOAP API for checking availability, submitting a registration, and updating records. So the honest answer to "does this registrar have an API" is, for almost every registrar on the market: yes, and has for years.
This is a companion discussion topic for the original entry at https://namefi.io/r/en/blog/agent-native