what language uses "fi"

That is a script written in bash shell.

The piece of code is Unix shell. But the answer to the question

what language uses “fi”

is a bit longer. The usage of mirrored words, like if and fi or case and esac comes from Algol, for a nice summary see comparison of languages. It was Stephen Bourne who carried this from Algol to the Unix shell, he worked first on Algol, later on sh and adb of the early Unix systems. He favored this syntax so much that even the C code he wrote for sh and adb looks like Algol thanks to a bunch of preprocessor macros. The curious can have a look at the 2.11BSD source code of source code of sh or adb. It compiles as C after all. So even in C one can find FI when going back a long way in history.

Those are used by Unix Shell Scripts... See this and this.