Intersections have a number of possible paths through them. Where those possible paths cross is called a conflict point.
Canada drives on the right. That means that right turns only do not entail any conflict points, except for a merge into the lane you are joining. This means you only have three things to watch for: pedestrians, moose, and oncoming traffic in that lane. That is the rationale behind allowing "right on red" - given the de minimis number of conflict points involved, the driver workload is reasonable.
As a matter of policy they allow 2 lanes of right on red, but that's not your question.
A "left on red" isn't going to work as a general rule, because of a much larger number of conflict points, mostly the worst kind, crossing conflict points. Is this too much workload for the driver? Yes - we know that, because that was the whole reason why the intersection was upgraded from stop signs to traffic lights in the first place! So a general left on red is unworkable.
However, one-way streets to the left create a special situation. From a one-way to a leftward one-way has no conflict points except the "merging" one discussed with right turns. As such, "left on red" is allowed there. This is the situation being discussed in your first link. The first link isn't referring to left turns onto two-way streets.
This isn't relevant to this conversation, but from a two-way to a leftward one-way arguably creates this favorable situation again; while there are crossing conflict points, they are only with your own street's traffic which is held by the red light. As such, some jurisdictions allow left turns from a 2-way to a 1-way. Alberta is not one of them, probably due to moose :)
The simplest way to think of this is, "you are allowed to turn into the nearest lane to you, if you don't cross any lanes at all", and in Alberta 2 lanes can do this at once.