An earlier USPTO reference:

> Description of downloadable API software from http://www.geocod.io/guides/on-premise/, accessed 09/08/2020

They mean they provide a Docker container image that can be downloaded and run on-premise. The container exposes an API for performing task X.

If I had to guess I'd say it's a library/SDK.

I wonder if the trademark application reads that way, or this website made it up?

Makes no sense, probably they meant that there's an API endpoint where you can get, i.e. download, information about the status of blockchain transactions.