So in your opinion the UK and all other ex Commonwealth countries like NZ Australia and Canada where the Queen is the head of state are not democracies either.
In a simple answer. YES! Democracy means choosing a leader via the democratic process of voting.
These countries do not process that right as per Germany, France, etc. So they are not true democracy in the pure sense.
The fact, the queen does not interfere with elected prime minister is irrelevant. She still technically have that power. She just choose not to exercise it.