May I understand that
"John really hates it when someone stands over his shoulder while he's texting, on the computer, or just standing over him period"
"John really hates it when someone stands over his shoulder while he's texting, on the computer, or just standing over him."
So what is the context/background of the original sentence?
The writer spoke to his secretary, who typed exactly what he said. And the secretary typed "period" instead of "." carelessly?
No, it's a colloquial way of saying "without any qualification", and it's usually said after a longer description. For example, I might say I don't like eggs in salads; in fact I don't like eggs, period. I'm taking back the qualification 'eggs in salads' and saying that in fact I could have ended the sentence there: 'I don't like eggs.', and that would have been just as correct.
Just to expand on EB's good explanation -- and fine egg-salad example -- I'll reword the original sentence just so Wishfull is clear. I believe there are three actions, so it would read like this:
"John really hates it when someone stands over his shoulder while he's texting, or when he's on the computer -- or just standing over him, period (no matter what he's doing)."
Note the comma before "period" -- there is a slight pause before the finality of saying "period." Also note that you can use the BE "full stop" in the same sense: I don't like David Copperfield; in fact, I don't like magicians, full stop. (Or "period.")