I think you're conflating right and left with authoritarianism / anarchism.
Anarchism can be left wing (anarcho-syndacalism) or right wing (anarcho-capitalism).
And capitalism is not the opposite of anarchy, capitalism is definitely a form of anarchy.
Capitalism can be defined as `an economic system based on the private ownership of the means of production and their operation for profit`.
Capitalism and free markets can't work if a strong government keep interfering, disrupting supply and demand and stealing profits - which is clearly visible in all the economic crisis we've seen in our recent history.
The opposite of anarchism is authoritarianism, which can be left wing (socialism or communism with publicly owned goods) or right wing (fascism, nazism - which comes from national socialism).
Now, large corporations benefits greatly from authoritarianism, because a strong central government is a single point of failure that can be lobbied and corrupted.
Why do you think middle class individuals pay half of their paychecks in taxes while big corporations pay nothing with fiscal loopholes?
Therefore, I think it's rational to assume that the environment in a large corporation is going to be leaning towards authoritarianism and promoting authoritarianism.
You can also add the fact that universities are increasingly left leaning and people in large corporations (and big tech in particular) tend to have higher level of education.
Of course, it's not great PR for the companies and it's not an easy sell on people, so they will need to masquerade their authoritarianism by saying appealing to people's emotions and saying that taxes need to be paid to "redistribute wealth to poor people" or to "protect our country from $external_threat".
The two party system serves as a way to illude people they have a choice and so that they can blame bad things on the other party.
Those of us who are lead on by nurturing emotions or economically comfortable enough to donate money will lean towards Democrats and believing the victimhood of minorities. Those of us who are poor or wants a smaller state will edge towards Republicans. The percentage of libertarians is so small, it's not even funny.
In reality, both Republicans and Democrats just kept increasing their spending and their power - and there is no sign of stopping. The USA are the largest employer in the world.
Because of these factors, I believe people and articles from large corporations will tend to have a left-leaning bias, which fits perfectly well with this left leaning article and it's not its opposite.
Ultimately, I agree with your analysis of the labour party: I can't think of any "left wing" party in the western world which is left wing economically - and this is because socialism has been proven not too work over and over.
The only meaningful difference between left wing and right wing parties nowadays is in the direction in which they edge (more taxes / less taxes) and where they stand on personal freedom issues (freedom of speech, gay marriage, etc).