Sigh, I just can't resist the urge.
So, first issue. You should probably provide a source for the picture, because you saying it's a left-wing individual cannot really be verified otherwise. Though I agree that the individual probably considers themselves to be left-wing. I agree that the picture is bad, though it's not for the same reasons you do.
So, what are left-wing and right-wing politics? In essence, that has to be answered first before you even begin to respond to the matter at hand. Generally, left-wing ideas support the notion of equality, while right-wing ideas support the notion of inequality. So, that's why at the far-left spectrum you have communism, which supports a transformation into a classless society, while at the far-right you have fascism, including Nazism, which supports the notion of a genetically superior race that is inherently meant to wipe out the lesser races for a "pure" society. Accordingly, these ideas evidently necessitate an economic component, as wealth/relation to labour is a massive component to equality/inequality.
I know a lot of people try to separate the two, but as I tend to have a materialist view of human relations (the belief that society has mainly been formed by material conditions/people are mainly motivated by material matters, rather than ideological ones) I view it as impossible to separate social policies from economic policies. So, where does that lead us? Well, let's talk about the economic system in which these games were produced. The United States, the United Kingdom and Japan, the countries where the majority of these games were developed, have a capitalist economic system. Indeed, virtually the entire world does at this point. Now, why is this important? It's because capitalism is an inherently unequal economic system. It is predicated on those who own capital/property using their capital and property to increase their wealth, while those who do not have the capital to live on their own require working for those who do. This is important, as evidently with video games also conforming to that capitalist framework, there's evidently going to be a pro-capitalist/right-wing stance. That is the norm as it stands, and that influence seeps deep into the subconscious to the point that you'd have to actively evaluate and confront it to root it out (though it's impossible to ever do it entirely).
Now, onto the picture itself. I don't think the person who made that really understands what left-wing and right-wing really mean. A major red flag there is the distinction between liberals and conservatives. Unlike how a lot of Americans tend to view of it, the liberal-conservative spectrum really isn't left vs. right. The reality is, both liberals and conservatives adhere to a dedication to the preservation of capitalism. The voting affiliations criteria makes no sense either, as both the Democrats and Republicans share a lot of the same policies/platform. The Republicans are definitely worse/more-extreme, but as it was made clear with this year's primaries and Joe Biden's platform, even the mere hint of more leftist ideas are met with scorn by the Democratic establishment (anti Green New Deal, Medicare for All, etc.) The fact that these initiatives, which don't even advocate for overthrowing of the current system, but rather reform within it, are being shot down is evidence enough that the Democratic Party can't just equal left.
So, with that being done and over with, I'll just highlight some issues I find. The first the immediately popped in my mind was Spider-Man. Why is that left-wing? Your main ally is Yuri Watanabe, a police officer, and throughout most of the game you're fighting random criminals. You're actively trying to uphold the status quo. On the other hand, Grand Theft Auto: San Andreas is in the right-wing column, despite the main antagonist being a corrupt police officer. In that case, you're actively fighting against the corrupt police establishment. I know, I know, it's not like CJ is some communist promoting a worker's/peasant's revolution to overthrow the bourgeoisie, but I just found the choices curious.
In doing it the way they've done it, it also creates contradictions. Take Super Smash Bros. Ultimate, for example. If sexualization of characters/diversity was an important factor in their decision, why is that in the left-wing column? The game lacks a lot of representation for ethnicities: dark-skinned characters are very sparse, let alone the LGBT representation in the game. The game's roster leans heavily male as well (come on Nintendo, give us more than just Min Min for DLC! You've still got Dixie Kong, Urbosa, Lip, etc. in your own catalog, not even to mention iconic 3rd party characters like 2B, Jill Valentine, etc.). Not to mention that characters like Bayonetta and the Luminary in it, characters who originate from games in the right-wing column.
So, overall, I think the premise of this list itself is flawed. It makes false assumptions on what left/right-wing means, and even within its own rules it doesn't seem to follow it very consistently.