I have won a prize.
This is win in the present perfect sense.
I heard about him having won a prize.
This is kinda-sorta win in the present perfect sense in gerund forum. It means he has won a prize, but it's converted to a gerund form so it can be an object of a preposition.
I'm sure I made someone with higher rep than me angry at saying that gerunds can have perfect forms. I don't really think gerunds can actually have perfect tenses - because A) they aren't even pure verbs and B) it doesn't work at all with past perfect.
What I think is really going on is something like this:
I am having lunch now.
I am having my nails done.
I am having my car repaired.
A meaning of have is "to take in" or "to receive or undergo an action."
I am having my clothes tailored = I'm receiving the action of "clothes tailored" from someone.
So:
I heard about him having won a prize = I heard about him having undergone the action of "win a prize."
I haven't been there in two years ... I wanted to know about him not having been there in two years = I wanted to know about him not having undergone the action of "being there".
Given the context of the original statement you want to paraphrase, you should not use either term.
The specific language you want to paraphrase is
I think it can be due to our upbringing. We want what we want when we want it.
You've proposed
today’s teens are much too pampered and as a result, lazy.
You've got a great start with reformulating the sentences so that you can replace "due to" with "as a result". You have also (like the narrator of the original piece) paraphrased the second half of the quote as "lazy", which works fine.
Your sticking point is how to paraphrase "our upbringing". You have proposed either "pampering" or "spoon-feeding" as replacements, but neither is really appropriate here.
When paraphrasing someone else's words, it's very important not to mis-characterize the original meaning. In this case, the original speaker talked about "our upbringing" and its results ("lazy" and "want what we want when we want it"). But she did not specify what aspect of rearing caused these result.
You have inferred that these lazy young people's parents were "pampering" or "spoon-feeding" them, and that has caused them to behave this way. But perhaps, instead, Ms. Benoit meant that she and her peers had been particularly deprived for most of their childhoods, and now that they don't have to work as hard they don't want to. That scenario might not seem as likely to you (it doesn't to me, either) but the original statement leaves open the possibility.
So, what should you use?
Look for a neutral synonym for "upbringing", or just use "upbringing", and then leave the specific deficits of this to the imagination of the reader (like the original speaker did). You may need to rearrange your sentence slightly to make this work. I would suggest something like
today's teens are lazy as a result of their upbringing.
or
as a result of the way today's teens were raised, they are lazy.
or, to stick as close as possible to your original structure,
today's teens were raised to be entitled and as a result, lazy.
Note that in that last example, I have substituted the adjective entitled for the statement that teens "want what [they] want when [they] want it", as suggested by Rhythmatic. That works, since you actually do have two descriptions of the young people in the original, and you were previously using the single word "lazy" to stand in for both. What we don't have is a description of the teens' parents' parenting style.
Best Answer
The sentence above uses the gerund "having" to form a gerund phrase which is the object of the preposition "about". The sense of "having" in this sentence is causative rather than possessive.
The sentence above uses the gerund "having" to form a gerund phrase which is the subject of the matrix clause. The sense of "having" in this sentence can be considered as obligatory rather than possessive.
If I understand your question correctly, you want to know whether the gerund "having" is only used for the possessive sense of the verb "to have". These two counter-examples show that the possessive sense is not the only possible sense for the gerund in question.