Robert Roode, Samoa Joe, Eric Young, and Austin Aries were great but I don't think their departure was as significant as AJ Styles. For years Styles was always billed as the face of TNA, and was their franchise guy, the guy who people identified with with when they thought of TNA. He was basically the John Cena of TNA. Even at his low points in TNA, people still recognized Styles and he was always an important part of the show. The word phenomenal could not have been used better when describing Styles, because he was phenomenal in TNA and was the guy who TNA could rely on the most. He could give anyone a great match, could go between the main event or mid-card, and was very popular with TNA fans, but there's more to it than that. When Styles left I felt like TNA lost a part of them in a way, and I don't think TNA has been the same ever since. When you lose your franchise man, your MVP, the face of your promotion, that's when you know things are all fucked up. TNA can try to replace him, and yeah they had guys like Kurt Angle, Jeff Hardy, and Bobby Lashley etc, but I think Styles was irreplacable. He's one of the most influential guys in TNA's history, and the fact that he didn't come from WWE but was a homegrown talent is what's special about Styles. Styles could very much have been the first non WWE/WCW guy that they could make into a top star, he was symbol for TNA, and when he left so did TNA's heart.
Roode was great, especially during his year long title TNA World Heavyweight Championship reign, but by the time of his departure, TNA had kind've moved on from Roode and were focusing on other guys, and Roode hasn't been much of a presence in TNA in his final days I don't think. So his departure was kind've "Meh". It wasn't as significant as Styles' departure though.
Samoa Joe, most people on here will agree that Joe could have been a big star for TNA, and was red hot at one point, and had TNA had stayed behind him maybe things would be different. But when TNA dropped the ball with Joe, Joe just became another fixture on the roster, and never got his momentum back. By the time his left, there's wasn't much left of the old Joe we knew and loved. For that reason I don't think his departure was as significant either.
Eric Young, Young was a great talent but for most of his career he was always the supporting guy. For that he kind've falls under the radar a bit. Don't get me wrong he's contributed to TNA in his own way, and deserves some credit. But Young wasn't as big as AJ Styles was, when he won the TNA World Heavyweight Championship, most people shitted on it and thought it sucked. Some people say that Young has been doing great work recently, and I don't doubt that because he has. But Styles was still more significant.
Austin Aries, Aries is kind've a strange one because his time with TNA has been good, but not great. He's had his moments and matches, but a part from that, Aries was kind've already done by the time he left TNA. TNA didn't seem to care all that much about Aries by the end of his run with them.
Anyway I just chose a select few names to address because they were brought up on this thread. I'm sure there are other names I could mention but i'll leave it at that. Nonetheless, I do very much think AJ Styles' leaving was the most significant loss to TNA, and i'm not being a fanboy by saying that because in all honesty I was never a huge fan of Styles but I give him credit where credit is due. He was an important part of TNA, and was basically Mr TNA. Just looking at how he's done since leaving TNA shows what TNA have lost in Styles.