Go back to the video, and pause exactly when the elven armor shows. Look closely.
The elven armor ONLY shows protection for the upper body, meaning that IF that included the greaves, then you would feel pretty cold around your legs.
Thus, the better conclusion would be no. Just because it wasn't shown, doesn't mean it's not there.
Don't worry, with over thousands of armor pieces, there has to be greaves.
That shot of the Elven armor is exactly how it looks if you would take it out of your inventory. Out of the inventory, I doubt the armor model would have both the greaves and the cuirass. Just look at Oblivion and Fallout 3. The cuirass models, or full-armor models from Fallout did not contain all the different pieces such as pauldrons. Only the chest piece. Bethesda wanted to keep the models condensed when they were in the worldspace. For example, if you drop a full suit of power-armor on the ground in FO3/NV, the model is only a small piece of the chest armor.
Looking at the Elven armor in the inventory again, it is a condensed version. Just look at the chainmail pieces hanging on the bottom and the surrounding thigh armor. http://cdnstatic.gamesas.com/akqacms/files/tes/screenshots/Cave01_wLegal.jpg screenshot shows them, only they are much larger than the condensed version of the Elven armor model shown in the inventory (or independent in the worldspace). The screenshot shows those pieces covering all of the thigh, which is greave territory. I think it's safe to assume those are the greave pieces.