The point is to say it's an error in an automated system, rather than a human who decided to intentionally send out notices to 120-year-olds. Of course humans programmed the system, but they surely didn't mean to program it to do that.
And more importantly, the humans who programmed it probably don't work for the selective service. Obviously all "computer errors" are technically the fault of a human somewhere down the line, but in common usage it means that "I didn't make a mistake, the computer didn't do what I told it to do".
That would be a pure hardware error. For example a cosmic ray hitting a cell the DRAM and flipping a bit. Or maybe the Intel FP-Bug, could also be a computer error.
Anything else in software is a programming error, but not necessarily a programmer error, since it might start with wrong HW specs, compiler bugs, etc.