What a fascinating list. But it begs the question, what is a parliamentary democracy?
Canada would be a French, Russian, Japanese, or German colony today if it weren't for us, and she has the nerve...
A parliamentary democracy is a government like Canada and Israel. A federal republic is a government like the United States and Russia.
Typical features of parliamentarian governments include non standard election cycles, weak or non-existant chief executive, party control of seats, and multiple major parties. The party or coalition of parties that controls the parliament picks the cabinet ministers. Thus one party or coalition always controls the entire government and the opposition party or parties (such as the Conservatives in Canada) are completely powerless.
In the USA, the terms of the President and Congress are fixed, and it is common for one party to control Congress and another to occupy the White House. In nations such as Canada, there is no separate election for the Prime Minister or other executive. The only election is a local election for a party representative to parliament. That said, there is no way to "split a ticket".
The best way to describe it is that in parliamentary democracy, the parties created the system. In a constitutional republic, the system created the parties.