This was not Yang Gang being melodramatic, but his true nature.
Abandoned by his parents since childhood, he'd always felt a lack of security deep down. He yearned to be needed by others, because he believed at least it could justify his existence; this had been a major reason for his entry into the world of the Bounty Hunters.
At the end of the day, all Yang Gang wanted was to prove to his parents who'd abandoned him - that he wasn't worthless.
The lad might appear nonchalant on the outside, but he was very fragile and sensitive inside. When he felt unneeded, his mood would plummet.
Truth be told, Yang Gang's character made him unsuitable to pretend being a wealthy heir. Although he was extraordinarily talented and excellent at everything he did, in essence, he was still a depressed loser at heart. But because of this loser-ness, he'd go out of his way to help people who had little to do with him. A real wealthy heir wouldn't risk personal harm to help others.