Tried to compile with the Makefile they have, but it fails saying icc, ifort not found -- meaning they want this to work only with their own compiler. Is this intended or am I missing something?

Given that it was just opensourced it's highly probably that it was developed only against Intel's own compiler. Those who want it to work with other compilers are now able to contribute code for that themselves, it's not Intel's responsibility to do that (though they certainly can if they wish).

According to the README, gcc can be used by running "make compiler=gcc". But it also says it's only supported on Linux...

It makes sense that they built it with their own compiler by default.

In any case, I wonder if clang could use this to jump start its OpenMP support.

Please Clang developers, we need OpenMP in Clang so bad!

A lot of the FreeBSD ports that are stuck on GCC are stuck there because of OpenMP for sure, or at least lose performance on clang...OpenMP on clang would be nice indeed.

As someone who isn't a compiler developer. What effect is this going to going to have?

If your code is using OpenMP, and this library is faster than your current OpenMP runtime, then using it might speed your code up a bit.