Storyline, Explained (A LOT OF SPOILERS)
I enjoyed this game; obviously, it's not for everyone. This is what I can gather of the story line, which is being told achronologically. Feel free to add to this or disagree.
The player is Citizen Abel (a character the creator uses in his series), and here he is one in a three-person friend-slash-criminal gang during the prohibition era in the fictional country of Nueva Aires. As for the other members of the trio, Anita is a demolitions expert, sharpshooter, mechanic, and confectioner; she has a robotic arm and leg. Borges is a forger, safe-cracker, pilot and also apparently the best man at a wedding you attended. It seems that this trio has planned a smuggling operation by air and they will pilot their own plane, but have to get through the airports. From the manual, we can gather that this trio is being reunited for this operation after many years apart ("And here they were, meeting again after seven years, albeit under different circumstances.")
In the prelude to the game, we see them at their hideout, which is located underneath a bar, before this major operation is about to happen. Their hideout is littered with ammunition, fake passports, plans, alcohol -- everything alcohol smugglers could hope for. Once they get to their plane/boat, they leave for their big heist and the prelude fades out.
Jump to the opening scene. The operation has gone terribly wrong and both Anita and Borges have been shot (apparently by each other) -- a soft clicking sound can be heard as Anita keeps trying to shoot you, even with her empty-barreled gun. You're in some sort of cargo hold of the airport. Outside, "wanted" posters for Borges line the walls. You need to make your escape, but Borges is badly injured. You hoist Borges onto your shoulder to save him, load him into a luggage cart and are making your way through the airport terminal while a series of flashbacks are presented as you think back to how you ended up here.
The flashbacks take us back first to happier times. Anita is seen peeling oranges looking out on a balcony as you get out of bed. Anita has all her limbs in tact, and we can gather from this and later clues she was in love with the player and was involved with him. The trio is meeting up to go to a wedding. As you walk into the wedding scene, you pass by a drunk girl near the doorway. The player drinks -- copiously -- during the wedding. As you leave, you see Anita stumbling back to the apartment and into bed.
Later, a very short flashback will reveal that the random drunk girl was at one point in bed with you -- possibly implying that after getting drunk, the player went home but ended up with the drunk girl that they saw and not Anita. At any rate, Anita was at some point betrayed or had her heart broken. In another flashback we find out what later happened to Anita's arm and leg -- the two of you were in a motorcycle accident when she hit a car head-on.
Presumably, her bitterness and unhappiness over some combination of her injuries in the accident and her heartbreak eventually led, years later, to this failed, or maybe purposely foiled, heist. The game and manual hint that she betrayed the group and sold out the other two in a deal with the police. (A card at the end has the quote: "Then it is agreed my little cilantro friend. Surrender the others and you shall be spared." And from the manual: "'Are we going to hate each other someday?" Anita remembered this from long-ago pillow talk. She couldn't recall who asked the question, but she remembered feeling that pinchy pang of knowing the answer. ")
Back in present time, the player and Borges are nearing the exit of the airport -- a pink door marked "Salida." They're engaged in a shoot out with a bunch of drones, which they take down, but leave only to be met with an exit surrounded by police. Miraculously, they get away, shooting as the police trail off behind them, but the player is distracted by his flashbacks. As he thinks about Anita's accident, he only refocuses in time to head into his own head-on crash.
The rest of the "game" is really the credits and is presented in the form of a museum display. Perhaps the trio was a bit of a Bonnie-and-Clyde-type gang and is now remembered for being an infamous group of smugglers. Possibly it's one display in a larger museum about the exploits of Citizen Abel. The Bernoulli exhibit, which explains the physics behind flight, hints that perhaps something about the flight technology they used was what made them so infamous.
The final, final ending -- e.g. the screen that the game closes on, perhaps what the player wants to remember -- is right before Anita's accident, years ago, when the gang was happily cruising together down the highway.