I definitely do not see Gria in Yugiri, at all. Grai horns are pretty distinct only ever seem to be one style which clashes heavily with what we know of Yugiri, not to mention the wings.. which there are none. Gria wings don't appear to be that flexible, not enough that you could wear clothing (cloth) over them and not see some kind of strange shape bulging on the back.
Secondly, a poll's a poll. It's just to garner an opinion on what fans wanted at that time. They likely used that information to give themselves and idea on what new races they could add to XIV in the future, just because a particular race won the poll doesn't mean that it is going to be the first new race you see in the game. But, be that as it may. I just went back to review that poll.
The "winner" was: Mammallian demi-beastmen (ex. a rabbit-eared race such as Viera from FFXII, etc.)
Burmecians fit that description. Maybe perhaps pure Burmecians would be a slight bit more beastial than humanoid. So how do you fix that? Well you give them humanoid hands and feet, and perhaps shorten their snout a slight bit. Boom, that can easily fit with what we see of Yugiri. Not to mention her face is purposely not visable/darkened-in/covered to add to the mystery until it's revealed. How do we know her nose isn't snout-like? It's covered up.
Even after saying all of that, I still think Burmecians normally are quite humanoid the main exception being their feet. Their hands are a matter of interpretation, some are drawn with huge hands while others are drawn with what look to be more normal digits.
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We know that Yugiri wears boots, so obviously she doesn't have the huge feet typical of Burmecians, and that her hands appear normal. I would explain this easily as the need for character models to be able to wear the armor in the game and have it be visibly identifiable.
I still don't see Gria, if those are horns they don't match the Gria style, and they are pointing the wrong direction. Even the one picture of a Gria I've seen with thicker horns still has them pointing the same direction:
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