The Printer(Parallel) port was traditionally at TTL levels. I think you are confusing the Parallel port levels with the Serial (Com) port levels, which are significantly higher.
However, some of the modern motherboard implementations of a Parallel port seem to wander down to as low as 3.8V in some cases. The high output on a parallel port pin will not source sufficient current to power your programmer. All that will happen is you will fry the port on the PC, both quickly and silently.
If you canabalise an old USB lead, isolate the data +/- (Green & White) lines and use only the V+ and Gnd (Red & Black) lines to power your circuit then you don't need the 5V regulator, but merely some decoupling. You could also steal the power from the Keyboard port if you so wished, it's easier to just use an old USB lead because of the ready availability of a socket on the PC.