Original Text: Although gamblers are the most prone to this, it equally applies to business during bubbles and to people who gain sudden attention from the public.
If I change the above sentence into the participial construction, is it grammatical correct? (To emphasize the meaning, I do not omit the conjunction.)
Although gamblers (being) the most prone to this, ~.
In order to reduce an adverbial clause, it must have the same subject as the independent clause.
'Although gamblers being the most prone to this' does not work grammatically here because it does not describe 'it': the two clauses have different subjects.
Here's an example where you can reduce the adverbial clause:
Though I was hungry, I didn't eat lunch.
Reduced to:
Though hungry, I didn't eat lunch.
In this case, the subject of both clauses is "I" so you can reduce one. However, in your example:
Although gamblers are the most prone to this, it equally applies to business during bubbles and to people who gain sudden attention from the public.
The subject of the first clause is gamblers. The second is it.
Therefore, this is not grammatically correct.
