By "left-wing" I mean "left of what that country considers center."
Liberals are centrist; PRI are not remotely left-wing or right-wing given that they're whores and can be good as both.
The Liberal Party in Canada is left by Canadian, American, and international standards. It's fairly safe to describe it as "left-wing." Furthermore, they probably have more of what you would consider "genuine" leftists in Parliament than the NDP, so they are therefore the "main left-wing party." Besides, if we go by your definition, then the "main left-wing party" in Canada is not the NDP but the Bloc Quebecois, which would be awfully silly.
I agree that the PRI is pretty awful. I expect that after the Communists are eliminated, it will be a race to the bottom between them and the CHP.