I really don't understand what's happening here. I think we use the term "API" and "server" differently. When I think of an API, I think of a library or something that I can link to. For example the POSIX API, or the P-Threads API. These are available in one way or anther from any language.
This seems to think very differently about APIs. As if APIs are somehow tied to a specific language? When they use the term API, do they maybe mean library?
I think that under the hood, the idea is that, if you want to do something, in another language (rather than just writing it in the language) you somehow generate a stub in both languages and then proxy through a (network?) connection?
To make this more complex, it seems that the proxy connections are not just on the local machine, but over the internet to another machine. Presumably you have to pay for this?
Am I right? This seems like a lot of effort to go through just to avoid figuring out how to do something directly. With really sucky performance implications. I guess it depends on what you're doing. Most languages support a foreign interface to C, so maybe that is a more sensible way to do this rather than setting up "servers" and tunnelling commands and data back and forth.
EDIT: I just had another look at the website. So, when they use the term API - it would seem that they mean some sort of an HTTP based web interface? The idea is that you have some kind of script that does something for you and you can query it from you local script. I still don't understand why you'd want to do this over running it locally?