I think I missunderstood that question. Since he used the 'or' in lower case and the other gates (NOT) in upper case I though 'or' was not a gate, but an option to use a or b for the example.The NOT operator is not distributive.
Do a truth table:
A|B|NOT( a or b)|NOT(a) or NOT(b)
F|F|T|T
F|T|F|T
T|F|F|T
T|T|F|F
if he said "NOT(a OR b)" I would have used a NOR gate.