Often (but not always) when people talk about a party or politician or political position being right or left, they are talking about its relative position compared to the distribution at hand.
Or, I guess sometimes they also might mean, like, some ambiguous combination of an idea of an objective left/right axis, along with the idea of a relative axis?
Regardless, people generally agree that, currently in the US, that the Democratic Party is “to the left of” the Republican Party. As such, for the purpose of practical communication, it is often useful to understand what people are talking about in terms of this way of distinguishing between the two.
I think the confusion here is mostly coming out of comparing US stances to globally expressed stances - both US parties are pretty right leaning on the global scale, but within the US left is democrat and right is republican - while people at the more extreme ends of the spectrum complain that, on the right, the republicans are too liberal and, on the left, democrats are too conservative.
The sort of interesting thing is it's really hard to be objective about this, if you were to measure where parties have stood on minority representation over history both parties today are astronomically to the left of any parties in the 1800s. I think the main thing we can sort of examine is where policies lie in relative comparison to the voting base and under that measure I'd expect that we have far more conservative and corporate representation today from both parties than the people voting - in a large part due to the political corruption existent in our system.
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Your second paragraph is closer, though in fact most people don't think about it at that level. They typically don't know or understand that the position is relative to the current distribution. When they say "democrats are on the left" they mean it in an absolute sense, and both the duopoly parties play that ambiguity up to their collective advantage.
The kind of voting system proposed isn't likely to change that.
