In the actual game, one scene between Amy and Gamma becomes very, very sad in retrospect. When fleeing the crashing Egg Carrier with Tails, Amy expresses hope that she and Gamma will meet again; but that ends up being the last time they ever see each other.
This is somewhat mitigated by the fact that at the end of Amy's story, she succeeds in reuniting Birdie with its family, which includes the Flicky that was inside Gamma. Gamma's Flicky also comes with Amy to help give Sonic what's left of the Chaos Emeralds in the Last Story. So in a way, they did meet again.
The cutscene prior to the battle is particularly chilling, as Gamma assesses the remaining units he must destroy, he looks through flashback images in his memory banks, one of Beta being redesigned... and one of himself. As he looks at his hand and designates himself, we know Gamma's fate is sealed. The lack of background noise aside from the gentle sea waves greatly compliments the somber revelation:
Gamma: Units remaining... (looks at hand) Gamma... Beta.
Gamma's theme itself becomes hard to listen to after you beat his story, especially that ending synth melody. In particular, once you make out what the distorted phrase is actually saying, it becomes outright chilling.
The prison cutscene. The supposedly intimidating robot confronts Amy for the bird, after she refuses, and in desperation, actually begs him to let it go. Gamma starts feeling pain from his new-found empathy, going berserk before letting them out of their cell and ordering them to escape. He slumps over the door switch, dumbfounded and guilt-ridden at disobeying his master's orders, though Amy shows sympathy and offers him her friendship before leaving. Gamma's heart-wrenching theme playing in the background helps none.
Amy, despite being locked away and under interrogation, can only feel pity for Gamma over his confusion over why she cares for Birdie so much:
Amy: (sadly) I feel sorry for you. Eggman failed to give you feelings.
After his brethren fail to collect Froggy, Eggman angrily teleports them out of his sight to be made into something useful; which, as Gamma discovers through Beta, isn't a pleasant process at all. Before he vanishes in front of Gamma's eyes, a pained Delta turns to look at him. While no dialogue is said, most sources and media imply that Gamma felt horribly guilty for unintentionally dooming his brothers.
Keep in mind, the E-100 units in Sonic Adventure were essentially siblings. Gamma was forced to kill the only people he ever cared for — with the exception of Amy and his creator Eggman (who he probably saw as his father) — for the greater good of saving the birdies from a Fate Worse than Death.
Gamma's recap text — from quitting the story and resuming at various points — actually has him describe his mission as destroying Robotnik's "Evil Machines" to explicitly rescue both the animals and the other E-Series. This suggests he regards them all, including himself, as villains at best deserving of a Mercy Kill, and adds another depressing angle to his fight with the upgraded Beta.
The worst of it all is how there is no one to mourn Gamma's death and sacrifice. His cohorts are all dead by his hand, Eggman vanished from the storyline but wouldn't take kindly to hearing that his robot had gone rogue. Sonic, Tails, Knuckles and Big knew him as little more than a generic badnik of Eggman's, and Amy never gets to see him again like she wantednote Bar the Sonic X adaptation, though that is just as heartbreaking when she outright sees Gamma and Beta kill each other. The only solace is, if Gamma and the bird are separate entities, that the bird family would likely be very thankful to him for doing what he did for their sake.
Tikal (JP): He has absorbed the power of the Emeralds... We must hurry and seal him inside the Master Emerald again!
Sonic (JP): Won't it just be the same as before?! His heart will still be bound by anger and sadness. He will never be free!
Tikal (ENG): Look! He's absorbed the Emeralds' power... he must be sealed in the Master Emerald, now!
Sonic (ENG): How can that help?! It won't change how he feels inside, will it? His heart will still remain in turmoil, and his anger just won't vanish! He'll just be trapped forever.
To think that Sonic wants to help save the God of Destruction is heart-wrenching to think about. All throughout the game, he saw Chaos as this huge enemy, determined to stop him and Eggman from destroying the world. To go from that over the course of the game, to understanding Chaos and wanting to save him from his fate is something that's both heart-warming and heart-breaking.
To say nothing of poor Tikal who sealed herself in the Master Emerald with him, just after her entire clan turned on her and the Chao and were destroyed by Chaos. The implication was that in her sorrow she intended to doom herself to that state again to save everyone, and while she given a more peaceful alternative, her original sacrifice still seemingly cost her mortal form.
Knuckles' predicament. He is forced to stay on Angel Island, guarding the Master Emerald. Bound by his duty to his species and to the gem itself, he is always tied to it, unable to stray too far. He will never be free like Sonic and Tails are.
In one of Big's recaps, he wonders to himself if Froggy keeps running away because he doesn't like him anymore.
As this Tumblr post points out, there's a reason Big works so hard to get Froggy back: because otherwise, Big would be all alone. He's not too familiar with the other characters yet; in fact, none of the other characters even refer to him by name throughout the game. Then, as Big tries to escape the Egg Carrier with Froggy, he comments that if "something" were to happen, there would be no point in Big rescuing Froggy, because he can't think of anyone who would come save them. In other words, if Big (and Froggy) had somehow gotten hurt or killed on the Egg Carrier, nobody might have noticed. This of course becomes Heartwarming in Hindsight after Sonic instantly sticks up for him against Chaos Six, showing someone will go out of their way to care.
Big's status as The Scrappy can also be this; he's just a common guy trying to get his frog back and the fans hate him for things that aren't even his fault. Someone give the poor kitty a hug...
Big: (frantically chasing after Gamma) No! Hold on, there! Come back, please! Gimme my friend back! I'm begging ya,pleeease!
As cheesy as it may seem, Tails' theme, "Believe in Myself" is sadder than the upbeat music would suggest. It's basically about Tails becoming disillusioned with his role as Sonic's sidekick and his own limits while trying desperately to make a name for himself. Then there's the implications of the chorus, which sound troublingly like Tails wanting to reunite with a departed loved one.
I wanna fly high, so I can reach the highest of all of the heavens. Somebody will be waiting for me...
Come to think of it, there's the (possibly related) implication in his backstory that he's an orphan...
The flashback cutscene of Tails meeting Sonic for the first time, which plays after he and Sonic are separated after the Tornado is hit by the Egg Carrier's main cannon and crashes. He wanders through the jungles alone and forlorn before Sonic speeds right past him. Tails follows him, trying to keep up. No words, only feels. The sad piano theme music doesn't help either. Doubles as Heartwarming, though, when the young fox wakes up and muses aloud about how much he's grown since he first met Sonic.
Tails: Wow, that dream brought back memories! (quietly gazes up at the night sky) I owe so much to Sonic.
It's also sad from Sonic's side of the events. After falling from the sky and landing in the Emerald Coast, he sees absolutely no sign of Tails anywhere, and sadly wonders if he's alright. He doesn't get to find out until Tails shows up flying the Tornado 2 a good while later in Red Mountain; so for all Sonic knew at the time, his best friend might have been badly hurt or even outright killed in the crash.
Sonic: Tails... Tails?! (sadly) Oh, I wonder if he's okay...?
being a slow, piano-based reprise of his theme.