(a) The post was created by scammers looking to make a quick buck off the tragic death of a beloved entertainer.
(b) The post was created by scammers looking to make a quick buck off the tragic death of the beloved entertainer.
would be meaningful and grammatically correct sentences. However, they do have subtle differences in connotation and emphasis. Specifically:
In sentence (a), "the tragic death of a beloved entertainer" describes an instance of a general class of events that the scammers were exploiting. The knowledge that the specific entertainer in question was Robin Williams, although clearly evident from the preceding context, is not actually required to make sense of the sentence.
In particular, the adjective "beloved" in this sentence serves only to restrict the class of possible referents — that is to say, its function is to note that the scammers could not have similarly exploited the death of a completely unknown or a generally detested entertainer, since most people would not have cared enough to watch the video. In carries no significant authorial opinion on Mr. Williams, beyond implying that he belongs to the class of well known and liked entertainers whose death many people care about.
In sentence (b), however, "the beloved entertainer" must refer back to some previously mentioned (or otherwise relevant) entertainer, of which, in the context you quote, there is only one.
Specifically, the adjective "beloved" in this sentence is functionally redundant: simply writing "the death of the entertainer" (or even just "his death") would be sufficient to unambiguously identify him. Thus, the redundant inclusion of the adjective "beloved", together with the definite article "the", comes across as particularly emphatic — the writer could've omitted the adjective, but chose to include it anyway, as if to emphasize just how beloved they feel Mr. Williams really was.
As for your second question, why couldn't the sentence read:
(a*) The post was created by scammers looking to make a quick buck off a tragic death of a beloved entertainer.
instead? Well, the simple answer is that it's because people die only once, so each person only has a single, definite death, which therefore takes a definite article. Now, this is not a hard-and-fast rule, and one could regard sentence (a*) as valid, but at least to me, it just doesn't sound quite as natural and idiomatic as the alternative phrasing (a).
What might confuse your ear is that, even if you don't consider sentence (a*) idiomatic, the following sentence is still perfectly fine and natural:
(a**) The post was created by scammers looking to make a quick buck off a tragic death.
Here, using "death" with an indefinite article is fine, since the sentence is just referring to one, unspecified death among the many thousands happening every day. However, as soon as you start referring to the specific death of someone — even if the "someone" is just an unspecified "beloved entertainer" — using an indefinite article for "death" starts feeling awkward.