There’s really nothing wrong with this sentence that you presented:
“As is vividly depicted in the cartoon, two people are playing football.”
It’s a perfectly grammatical sentence that denotes a stage of an action or situation as captured in a stationary or nonmoving illustration.
We can also render that sentence in this other way that you suggested:
“As vividly depicted in the cartoon, two people are playing football.”
This version is actually an elliptical construction of the first sentence above, one that eliminates the verb “is” in the coordinate clause “as is vividly depicted in the cartoon” without changing its meaning.
Now, about your other question: Is the following version of that sentence also correct?
“As being vividly depicted in the cartoon, two people are playing football.”
Yes, that sentence is also grammatically correct, but its use of the progressive verb form “being vividly depicted” denotes a slightly different sense and situation. It means that the action being depicted in the cartoon is in progress right at the very moment of speaking. It’s either that the cartoonist is currently drawing the cartoon and the observer is describing the process, or that the observer is describing the action that’s currently unfolding in an animated cartoon show.
In sum, royljc, all three sentences are correct for their respective contexts.
