Arya survives simply because she has the will to go on and more importantly was saved by Lady Crane who treated her wounds.
CUT TO: BRAAVOS - LADY CRANE’S APARTMENT
ARYA is lying in bed. LADY CRANE sits beside her, treating her wounds.
ARYA: You’re good at that. Where did you learn?
LADY CRANE: I’m a jealous woman. I’ve always liked bad men and they’ve always liked me. They’d come home wherever home was that night stinking of some whore’s perfume.
LADY CRANE stands and carries her tray of medical supplies into the abutting room.
LADY CRANE: So we’d fight and I’d put a hole in them. And then I’d feel terrible, so I’d patch them up. I got good at patching them up.
ARYA is afflicted with pain from her wound. LADY CRANE stands and pours a milky white liquid into a glass.
ARYA: What’s that?
LADY CRANE: Milk of the poppy.
ARYA: I don’t want any.
LADY CRANE hands ARYA the glass.
LADY CRANE: Sleep is the only way you’ll heal. Trust me, if my soup didn’t kill you, nothing will.
ARYA takes the glass, stares into it, and then drinks it down. She lays back and LADY CRANE tucks her in. ARYA falls asleep. LADY CRANE touches her hand and dims the candlelight.
Game of Thrones, Season 6 Episode 8, "No One"
The director for the episode, Mark Mylod, explains that it is her will for survival that also helps her survive the attacks.
"One of the many things our writers are so great at is allowing our characters to be flawed," he explained. "Nobody is perfect, we all make mistakes all the time, and Arya nearly pays dearly for it. Thankfully her determination to survive is such that she is able to come through it. But it is a really close call."
Business Insider, 'Game of Thrones' director explains the crucial Arya scene fans have been obsessing over
It's also worth noting that we don't really know the extent of the wound Arya receives, it could be...
...and as such wouldn't really have been "too bad" respective to some other wounds.
Now just to expand on the counter examples you make for why Arya should have survived.
Robert Baratheon: Robert's death was engineered by Cersei Lannister and so it was all a set up so he would die. Add to this that Robert was then treated by Grand Maester Pycelle who was under Cersei's payroll it is no wonder that he passed away from his severe wounds.
Khal Drogo: He had more than just a scratch but it wasn't necassarily a bad wound. However, the Dothraki don't really have the same level of medical care as the rest of the world. On top of this we then have the fact that Dany convinced him to let Mirri Maz Durr treat him who then might have had a helping hand in his death.
Talisa - She dies pretty quickly so it seems obvious that her wound was a lot worse than the one Arya sustains.