Yes, it does. They made some additions to the character texture maps (mainly mouths) and greatly increased the rendering resolution of the polygon models, so they all look crisp when the game runs at 1080p. It's a huge improvement over the PSX version, even though nothing was technically remodeled.
They recently announced that they're doing the same thing for FFVIII, which I will probably also buy. There are screenshot previews available in every article about it. Compare it to the original; there's a big difference in the characters.
New PC remaster:
Original:
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