Arya continued the blind training until she could hold her own against the (sighted) Waif while blind - they're now well matched when Arya is handicapped and the waif isn't. So:
- Blind Arya can beat sighted Waif. With Waif using sight and Arya using only other senses, it's a close fight Arya can win.
- Blind Arya has lots of experience fighting the Waif. She is finely attuned to the sounds and patterns of the Waif's movements
- The Waif has (presumably) also been trained to fight while blind, but has always fought Arya while sighted. She knows all the visual cues for Arya's particular moves - but they're useless here.
So, Arya's extensive experience of the Waif's fighting style is 100% useful here, but the Waif's specific experience of Arya's moves is much less useful in this fight.
Arya's fighting a familiar fight she's fought countless times, while the Waif is blind-fighting against Arya for the first (and last) time.
Arya's also using a weapon (Needle) she's got heaps of experience with, but which the Waif has never faced from Arya. This is a big deal not just because it'll be a different experience, but also because Arya is left handed (fun fact: actress Maisie Williams is right-handed but taught herself left-handed swordplay for this role) and the Waif has mostly fought Arya while she was using a two handed weapon.
In real-life fencing, left-handers are tricky to defend against because attacks are coming from less familiar angles. This must be harder still if unable to see.
So, things that give Arya an advantage:
- Her blind-fighting skills are fresh and sharp
- She's mastered anticipating the Waif's moves without sight
- She's using her favorite weapon (Needle)
- She's very familiar with this particular enclosed room, and can use the walls and furniture to her advantage
Things that may give the Waif a disadvantage:
- We don't know how recently she's used her blind fighting skills. Presumably she can do it well, but she's likely to have less recent experience and might be rusty
- All her experience fighting Arya was while sighted
- We don't know how recently she fought an opponent who was using Bravo-style swordplay. Presumably (living in Braavos) she's familiar with it, but she might be rusty
- She's in an enclosed space she doesn't know and can't see, which is likely to make her even more vulnerable
- All her experience fighting Arya was with a two-handed weapon. She's never seen the unique blend of Syrio-inspired water dancing, Hound-inspired brutal pragmatism and Waif-inspired minimalism that later on (beware small season 7 spoilers) we see that Arya had developed.
This reminds me of what Ned said to Jaime about why he never fights in tournaments (from this transcript):
...because when I fight a man for real, I don’t want him to know what I can do.
The waif is unarmoured, unprepared for this type of fight, on unfamiliar ground against an agile left-handed opponent she underestimated, who has a
big sharp f*****g sword and remembers where the heart is.
Of course, as noted in a comment, Arya also has a massive fresh stomach wound that is probably infected from the stagnant, sewage-ridden city canal water she then swam in, plus the deadly fast-acting poison that the waif has unlimited access to and would surely have coated her dagger in as a matter of habit.
But, erm, that doesn't affect her fighting ability here because.... erm... Reasons