One could make the argument that omitting the Prime Minister from the list of leaders is actually correct.
You are mixing up leader with head of state. The latter can be a completely meaningless role fulfilled by a paid actor such as in our case, whereas the nominal leader may look like a paid actor, but tends to have actual power and some form of accountability.
I am not a native speaker - what is the difference between these two words?
The leader of a country is the person leading it, e.g. a president, prime minister, or similar.
Sometimes the term head of government is also used, which I think is usually the same as the leader of the country.
Hiding in fridges for a start.