This is kind of the tl;dr 30-second elevator version of it.
Hegel's Dialectic is at its simplest the belief in a positive idea (the thesis), a competing negative or contradictory idea (the antithesis), and the end result, a new concept that nullifies and replaces both the thesis and antithesis, the synthesis.
Social Marxists, cultural anthropologists, and other leftist thinkers have loved to rely on the Hegelian dialectic to attack Western thought for many years. Edward Said (a literature professor) wrote the famous book "Orientalism" that basically says everything that Westerners believe about the Middle East is pure fantasy, wish fulfillment, the Other; that which the West is not. The West is civilized, therefore the East is savage. Western women are chaste and virtuous, therefore Eastern women are sultry whores (harem fantasy). Western men are honorable, Eastern men are untrustworthy, etc. Said, incidentally, just built his book on the prior work of everyone's famous pedophile, Foucault.
Ok, getting to the point.
Today, why do leftists of all stripes love drag queen toddler time? Why do they love kids burlesque shows? To reference a post from today, why do leftists NPCs love cities and hate suburbs.
Thesis. Antithesis.
The left today is defined entirely by what the right is NOT. To be more accurate, the left today defines itself in opposition to their perverse imaginary view of what the right is.
The left believes the right is Christian, therefore the left exults in atheism, satanism, Islam, etc--anything that is NOT Christian.
The left believes the right is ignorant rural and suburban dwellers, therefore the left is modern and urban--anything that is NOT rural.
The left believes that the right requires strict gender roles and rules, therefore the left wants to tear down the very concept of gender.
The left believes that the right wants to kill all gay people, therefore the left wants to groom more children to be gay.
Edit to add: The left believes the right is irredeemably racist and white, therefore the left exults and honors anyone non-white over anyone white.
Edit to add: The left believes the right is male-dominated and patriarchal, therefore the left attacks anything masculine and praises the feminine.
Some of these points are a bit (but only a bit) exaggerated, but the point is that the modern left is an entirely intellectually bankrupt movement. It is a negative. It can only define itself as the opposite of the right.
You've actually got it entirely backwards.
Even the very foundation view of "left-right" politics is a purely Leftist construction of reality.
The Left-Right Dynamic comes from the physical location of specific political factions in the revolutionary council that ruled France during the revolution. The Jacobins and their allies were seated on the Left side of the room, and the people in opposition to them, including what would become the Thermidorians. The Jacobins were "Leftists", who were basically responsible for the Reign of Terror and had control over the entire government, which they had been subverting since the beginning of the Revolution, including driving out and threatening to kill Liberals like the Marquis de Lafayette.
The Jacobins asserted Rousseauian arguments: claiming knowledge of, and representation of, the "General Will" of France. And therefore, as Rousseau described, enforcing the General Will on anyone who dissented by means of force was a moral imperative. The Leftists thought the Reign of Terror was a moral imperative. Please understand that and it's implications. The "Rightists" were literally everyone who was in government but hadn't been forced out or executed by the Jacobins that were spiraling wildly out of control and covering themselves in human blood. Fundamentally, they were people we would identify as "Left Wing", because all the philosophical liberals, monarchists, and French conservatives were either dead, or have gone into hiding.
"Rightists" are literally everyone who has an objection to Leftist power. They are, by definition: reactionary. Which is why the Left calls "Rightists": Reactionaries and Counter-Revolutionaries. It's because they literally are those things, because the Left decides what the Revolution is, how it works, and anyone who disagrees is reacting to their aggression.
The Jacobins literally set the "tempo" of the political conflict, had establishment power, and had the initiative. The Rightists were the people who agreed with them in principle (including the murders) but didn't want to be enslaved to the Jacobins assertion of the General Will.
Very long story short, the Jacobins spiraled until they got themselves killed by giving the Rightists an opportunity to seize power from them, and purge the government. Historians like to pretend that the revolution entirely stopped there, but this is a Leftist lie designed to protect the inevitable result of "Leftist" revolutions. Once the Rightists seized power a strongman (Napoleon) walked in and took on the mantle of responsibility of the revolution itself, going so far as to declare himself emperor of the revolution. France was the Revolution, and the Revolution was Napoleon. Germany did something similar a century later.
Now, you are not wrong that the Left engages in a Higelian Dialectic, but this is because they are operating from principles of power alone. What you need to understand is that the Left is prepared to change any position in order to achieve power. It is not true that the Left are reacting to what Rightists are. As with France, the Left are seeking to destroy any power structure that they do not control. Then they decalre someone, or something to be an enemy.
Leftists have taken both sides of any conflict so long as it benefits them. Leftists both opposed, and supported, the European Union. Leftists both supported and condemned homosexuality. Leftists both supported and condemned white racialism. Leftists both supported and condemned farmers and people who lived in a rural environment. Leftists both supported (and invented) Nationalism, and also condemned it (sometimes in the same time period). Leftists both supported and condemned Trotsky. This is because the Left, as you noted, has no principled topical stance, as it differs from country to country, and time period to time period.
This is because, following from Rousseau: Leftism is a Philosophy of War.
Rousseau is insane and obsessive about destroying all structures of order in all societies in all civilizations because all civilizations are "oppressive", meaning they impose any restriction on conduct. Rousseau's concept of Free Will is to enact is other idea of the Noble Savage, who is just a perfect sustained, perfectly strong, and fully atomized individual who has no constraints of any kind. He asserts that the first moment someone, anyone, ever, imposed an idea of "this is mine": utopia was destroyed. So, all of that must be destroyed until we get back to that utopia.
That's literal madness, and is also so historically ignorant, he was mocked and challenged on this at the time, and he (himself) said it probably wasn't even true.
This utopia (being a utopia) may be achieved at any and all costs whatsoever. This is because civilization is always worse than the Noble Savage. There are no necessary restraints on his philosophy, because he is seeking to achieve utopia by... any means necessary. He asserts that since civilization is an oppressive force, and all institutions are marks of civilization; following the "General Will" will dissolve those structures. The General Will is a vague abstract concept of the population just unanimously agreeing on something that is only magically revealed by votes. When it is discovered by winning a simple majority in a vote, the General Will must be followed. In fact, it is a moral imperative to coerce anyone who disagrees into becoming in compliance with the General Will. Including exile, social pressure, starvation, torture, and death. That is why the Jacobins wanted the Reign of Terror.
WHEREFORE, since:
Then you've got an equation that makes a different dialectic. A Hegelian Dialectic is how the Left is presenting itself. But this equation is of a Melian Dialogue.
That Dialogue is from a story that literally coins the concept of: "The strong do as they will, the weak suffer what they must." Otherwise known as: might makes right.
Anyone who is strong enough to assert the General Will is morally required to impose that will on everyone, regardless of consequences, savagery, or violence. Tyranny is a moral imperative.
TL;DR:
So, no the Left are not defining themselves in opposition to the Right. They are defining the Right in opposition to them, and their position is whatever they say it is, because they said so.