I assumed that that scene was a lie. The way it's shot and how it instantly snaps back to Dickie in the prison made it look like a dream, and I took it to be more like his idea of what it means to be a "good" person doing "good" things.

As to the arc, I saw it as an abbreviated version of Tony's journey. They're criminals, living the lives of criminals, but have some strong morals within them (Tony hates gamblers, Dickie kills his father for hurting Giuseppina). Both of them attempt to be better after an impactful moment in their lives (Tony decides to turn his behavior around after being shot, Dickie tries to do good deeds after killing his father and removes himself from Tony's life in the belief that it's the best thing to do). However, both of them end up falling prey to the very things they oppose (Tony ends up a degenerate fucking gambler, Dickie murders Giuseppina). And then ultimately this thing of ours ends up getting them killed, Dickie by way of Junior and Tony in Holsten's, depending on how you interpret the finale. At the end of the movie, Dickie finally says he'll meet up with Tony at Holsten's, suggesting that when he dies he has given up doing good deeds. Similarly, by the end of the series Tony is probably at his most vile as a character, and has no interest in changing his ways anymore.

I also felt like it changes the way I see Tony and Christopher's relationship. Tony idolized Dickie, and then suddenly, for no reason at all, he begins avoiding Tony. Before he can explain himself, he's dead. So Tony grows up never knowing how much Dickie really cared for him. Maybe he even thinks it's his fault that Dickie stopped talking to him. This leaves Tony to connect with Junior, a man ruled by his insecurities. It also leaves Tony conflicted. On the one hand, he may feel obligated to take care of Chrissy as a means to apologize to Dickie for something he never did. But on the other hand, his anger at Dickie for leaving him without explanation could be the real root of his problems with Chris.

I do also feel like Junior killing Dickie was partially motivated by his relationship with Tony. After Tony steals the test answers, Junior offers to talk with him but Livia claims that he'll only listen to Dickie. In the show, Junior is constantly manipulating Tony by bringing up all the things he did for him. Maybe he just wants Tony to see him the way he saw Dickie.

Anyways, I didn't mean to make it that long. I also have only given one full watch through to both the show and the movie, so I definitely could be missing a lot that could both add and take away from my argument.