This is not defined in the Core Rules
The Players Handbook lists normal unarmed Strikes as 1 damage in the weapon table on page 147.
The giant does not have natural weapons, it has manufactured weapon attacks, and if it loses the manufactured weapon due to player action, it will be reduced to unarmed attacks, just like a character (unless it has some rocks to throw...). This is covered in the Sage Advice Compendium:
Are natural weapons considered weapons? Things designated as weapons by the rules, including natural weapons, are indeed weapons. In contrast, unarmed strikes are not weapons. They are something you do with an unarmed part of your body.
The DMG advise on monster damage by type of attack is this (page 278):
If a monster has natural weapons, you decide how much damage it deals with those attacks, as well as the type of damage. See the Monster Manual for examples.
If a monster wields a manufactured weapon, it deals damage appropriate to the weapon. For example, a greataxe in the hands of a Medium monster deals ld12 slashing damage plus the monster's Strength modifier, as is normal for that weapon.
Unfortunately, an unarmed strike is neither a natural weapon, nor a manufactured weapon. The section you cite above is also about manufactured weapons. Because there is no rule that tells us what the damage of an unarmed strike for a larger than normal creature would be, the damage of such an unarmed attack is left undefined.
Also note that the rule for multiplying the damage die by size is not a hard rule, it is guidance only. For example Baphomet is a Huge demon, but his weapon attack, a great glaive called Hearthcleaver that deals force damage only deals 2d10 plus damage bonus, not 3d10.
It would seem reasonable to apply the same size multiplier to the unarmed strike, which deals a default of 1 point of damage, for 3 damage.
It also would be reasonable to compare this to other Huge monsters that have natural fist attacks that are similar to unarmed strikes, such as the Giant Ape, which deals 3d10 damage.
Or it would be reasaonable to assume that rowdy giants have a natural penchant for fistfights and grant them the equivalent of the Tavern Brawler feat, giving them in combination with the size modifer a base damage die of 3d4. This latter option is apprently what was chosen for the hill giants in Storm Kings Thunder (Kudos to @Pepijn who dug that up).
I think that this latter option is the best one, as it has precedent in published materials.