I have a friend setting up this character, and we were not sure, since Half-Giants can use weapons upto one size larger.
RAW is Unclear
Powerful Build never mentions unarmed strikes explicitly, only mentions “wielding weapons” – and technically, unarmed strikes are (kind of) a weapon, and “wield” is mostly just the verb for “what you do with a weapon.” But you do generally need to have a larger-sized weapon in order to wield it, and nothing says that the half-giant has a larger unarmed strike, even if they could wield it without penalty if they did.
From the description, though, it seems like they ought to
Half-giants are described as being, well, very large. Their hands are large enough to wield Large weapons; that appears to indicate that they’re also large enough to deal damage as Large weapons in and of themselves. Yes, half-giants are not truly Large category – they do not take up a 10' square, nor do they have a 10' reach – but they certainly seem large enough for the small increase in damage that you get from being a size category larger for unarmed strikes.
And for balance, it should definitely be Large
There is nothing special about unarmed strikes that justifies making them the sole exception to the half-giant’s racial ability to benefit from larger weapons. They are actually generally weaker weapons than real weapons. So a half-giant brawler should use the Large Brawler column in Table: Small or Large Brawler Unarmed Damage to determine his or her damage. Even doing so, the brawler is a very weak class; even with this minor benefit, the character may struggle mightily.