I am incredulous about your lack of understanding. I think you are not so much interested in definitions as much as you are curious about MY opinions.
A work of art is nothing but interpretation and perspective. Any reaction to a work of art is an opinion.
I am flattered that you care. However, this dog don't hunt.
So, with this reply you are saying that my query about the definition of "leftist" art is ...
incredulous?
I only offer the following.
What constitutes art is in the eye of the beholder. The definition of art is controversial in contemporary philosophy. Whether art can be defined has also been a matter of controversy. The philosophical usefulness of a definition of art has also been debated.
Art cannot be defined, hence my question.
So, what is "leftist"?
Left, left-wing and leftist generally refer to support for social change to create a more egalitarian society. They usually involve a concern for those in society who are disadvantaged relative to others and an assumption that there are unjustified inequalities (which right-wing politics view as natural or traditional) that should be reduced or abolished.
I didn't need a definition of "leftist" as I am thoroughly aware of the common usage of the term "leftist", "left-wing", "lefty", etc. My question was its association with the word "art".
Leftist art would then be an image created by a person who identifies with leftist ideology. In my opinion, the image itself is practically meaningless without the artist's explanation of what it is supposed to mean. Unless we are simply looking at a still life of a fruit basket, then there is no message, just the style and skill of the artist is on display.
So, if an artist identifies with a particular political or sociological subculture, then the work emanating from that artist must be the expression of the same? So, Diego Rivera, an artist with whom I have little or no knowledge (I think I've heard the name before, but that's it), is a leftist and any work of art he completes is leftist art?

In the example I gave and the image you provided, the artist was leftist and his image conveyed the struggles and triumph of man according to his personal vision. It just so happened that Rivera's vision was diametrically opposed to Rockefeller's personal vision, so the mural was destroyed. Rockefeller being a capitalist and Rivera being a communist and all.
Oddly, I gained no feeling of leftist art from the example you gave. I simply see a few slices of humanity crunching through the mechanisms of life and through the lenses of time. Certainly, in the lower-right corner I see the red flag waved as a symbol of workers, who are largely a group of white men -- not very diverse, in opposition to the lower-left corner which is a bunch of spectators who are diverse in age, sex and race, but it even includes animals. The two sides are either viewing the same mechanisms of life, viewing each other or in opposition to each other. I'm not really sure. If I find anything politically telling from this portion of the work it is that the most diversity occurs on the left (leftist?) and the least occurs on the right, but the right side is waving a red flag, which is a leftist symbol. Offset from that is the upper corners which show an army marching to war (offensive or defensive is not clear because it looks like planes are bombing from behind) and it appears that the Christian god figure is providing power to the war -- a rightist expression on the left side of the painting. Meanwhile, the upper right is another set of non-diverse workers (except for sex) wearing red.
Now, in all of this, the physical positions of the groups are in the corners opposite of their political directionals, but they are facing the opposite way, also. Or, are they all staring at the center? Perhaps they are staring at the machine of life and time that keeps going no matter what else these groups or their competitors do?
So, Diego Rivera is leftist and says that this work is leftist art? Funny, I don't see it that way at all. Even the title of the work implies no particular point of view because the only thing at the crossroads is a center point. In my opinion, if there is any political message to this work it is that those who think they are on the left might find that they are actually on the right, and vice-versa. Or, that when one goes sufficiently far enough to the left or right, one ends up in this strange area that sometimes referred to as "libertarian". Libertarianville sounds like nirvana, but it isn't (IMNSHO). It can't be. Libertarianville has only one rule which is that there are no rules. Ultimate freedom. Libertarianville is where the liberties of one can suppress the liberties of another, and frequently do. Ironically, all of the things depicted in the work have rules, whether it is physics, biology or sociology.
If Man at the Crossroads is leftist art, it is only so in the mind of its creator. If the meaning of art is in the eye of the beholder, the work only says to me that we should all work together, not in opposition, and I don't find that has any other political message than compromise.
On the other hand, Norman Rockwell idealized[1] the conservative point of view. His illustrations evoke a sense of nostalgia ...
Given my lack of knowledge of what makes art "leftist" or "rightist", I gave Norman Rockwell as an example of anti-anarchy, anti-chaos. Using the word as aptly as you did, Mr Rockwell apparently considered himself to be an illustrator rather than an artist. He conveyed images of life as he saw them, and his works were used to illustrate others stories or events. In other words, Rockwell could have been a photographer but chose to paint instead. As you indicated, his works are only viewed as "conservative" merely due to the passage of time, those who appreciate his work and pine for the time in the past when their lives were simpler (older people, generally). However, as an illustrator of life, Rockwell was not immune to any political perspective, including a "leftist", "liberal" movements, such as the civil rights movement. So, not all of his work appears like a family photo album. I am sure that many who pine for his "conservative" illustrations are unaware that he painted the word "nigger" in a painting that was displayed in the White House. Here is the work
The Problem We All Live With:

After all, who takes the time to immortalize their personal hardships?
Unbeknownst to many, Rockwell did -- or at least he did document the hardships of others. So, is Rockwell defining his own work or are the beholders? I ask this question because if an artist says that his or her work is one thing or another, that doesn't necessarily make it so. Of course, in the above painting, Rockwell is simply illustrating political discourse, but is he for it or against it? While I view Rockwell as someone who is illustrating civil rights in action, could he also be speaking to those who call blacks "niggers"?
So, you see...the question you ask is not very simple and I am not a scholar but I hope this has helped you understand what leftist art is, in some way.
On the other hand, if I have completely missed the mark...I await your correction.
Neither am I a scholar about artwork -- not in the least. While the creator of a work has a purpose or thought in mind, it is ultimately the viewer who decides the meaning of a particular work of art. Given the wide interpretation possible with art, it seems limiting to provide political categories to art.
PS: I only provide a caveat for Rockwell as an illustrator because some artists are prejudiced against illustrators as "artists". They simply view them as people who build images using the same materials as artists, but not expressing their own views insomuch as someone else's. This is much like carpenters who build homes with the same materials as "artists" but the work of carpenters is not considered "art". I provide no snobbery in either direction on the issue.