Would any other brainfuck compiler work without libc? Without the kernel? Without x86 microcode? This question has no meaning, in my opinion. What's important is that the printf statement is doing the logical work to calculate the next state of the machine.
I see what you mean. I don't know C, so I had no idea why the printf was doing all the work after looking at the code. I'm just wondering what all those other lines are doing.