No. Read the DMG. SOME NPCs are monsters, but only those you give monster stat blocks. Giving the NPC a monster stat block is 1 of 3 ways to make an NPC.
The NPC I am talking about is not subject to any monster "rule."
Go read the definition of "monster" posted by JG above.
"A Monster is any creature that can be interacted with, potentially fought with and killed .... The term also applies to Humans, Elves, Dwarves and other civilized folk"
The example you gave, was a creature, had hit points and presumably could be killed, so yes it is a monster. I guess something like an Unseen Servant or a major image could be an NPC that is not a monster, because those are not creatures.