I'm not 100% sure if this is completely official, but it appears to be similar to other instances:
Their Powerful Build allows them to be considered 1 size larger when it is beneficial to them.
Powerful Build: The physical stature of lesser half-giants lets them function in many ways as if they were one size category larger. Whenever a lesser half-giant is subject to a size modifier or special size modifier for an opposed check (such as during grapple checks, bull rush attempts, and trip attempts), the lesser half-giant is treated as one size larger if doing so is advantageous to him. A lesser half-giant is also considered to be one size larger when determining whether a creature’s special attacks based on size (such as improved grab or swallow whole) can affect him. A lesser half-giant can use weapons designed for a creature one size larger without penalty. However, his space and reach remain those of a creature of his actual size. The benefits of this racial trait stack with the effects of powers, abilities, and spells that change the subject’s size category.
Now reading from Alternate Form it has:
The creature retains the special qualities of its original form. It does not gain any special qualities of its new form.
Does this mean that if I am a Druid that wild shape into a Medium creature, and I try to Grapple I can be considered a large creature still? If this is true, I would assume the same would be true if I wild shape into a Large creature.
Best Answer
The half-giant monster entry lists Powerful Build as a Special Quality. Alternate Form explicitly lets you retain those, so yes, a druid with Powerful Build does retain that bonus, which is sizable. Powerful Build explicitly stacks with things that change your size, so if the druid used Wild Shape to turn into a Large creature, he would count as Huge for the purposes listed in Powerful Build.
See here for a list of options for obtaining Powerful Build. Note that all of them have positive Level Adjustment, which the homebrew lesser half-giant you found does not. Many DMs would balk at that. In reality, Powerful Build on its own probably doesn’t justify LA +1, but Wizards evaluated it as such. Level Adjustment is bad in general, but truly awful for spellcasters. And the half-giant race has nothing else of use or value to a druid, though use of the Primordial Giant template from Secrets of Xen’drik, at least, would make the half-giant more caster-ly (though still nothing particularly relevant to druids).