Intrinsics are function declarations that the compiler treats specially and maps directly to specific instructions for the processor.
Thus, it is the compiler vendor that determines what CPU instructions are available as intrinsics and their exact spelling in the source code. The CPU won't know if a particular instruction was given because the programmer called an intrinsic function or because the compiler decided that that instruction is the most appropriate for the non-intrinsic code that was written.
As intrinsics translate to processor instructions, AMD CPU's will support the same intrinsics as an Intel CPU if and when they support the same instructions.