I'm a Brit and have never heard "middle-end" used like that. "Middling", yes. "Middle-end", no.

And to answer the grand-parent:

building infrastructure that will help other parts of the project -- part of why I call myself a ‘middle-end programmer’.

It seems that the author is using "middle-end" in a manner analagous to the more common "front-end" and "back-end".

Exactly what this involves is not entirely clear, but building frameworks, perhaps.