That particular beer is a light ale and you can add watermelon extract at bottling. Place into your bottling bucket and rack your beer on top of it to mix it together, taste it, and add more watermelon to taste.
Checking out BBW website they actually use a naturally flavored watermelon extract. Real watermelon is mostly water so you would probably have to use ALOT if you wanted to steep that in a secondary to impart enough taste. I would love to make something like that this summer, thanks for implanting the idea in my head!
Primary 1: Whiskey Stout
Primary 2: Apfelwein
Bottled: Oat Red Ale, Peach Wheat, Strawberry Dirty Blonde Ale, Brown Sugar IPA
In line: Cucumber Summer Blonde, Kona Pipeline Porter Clone, Bacon Porter
The best yet: St. Nick's Dirty Stout (Vanilla Gingerbread Stout) - guessed at the recipe when boiling, didn't write anything down... DAMN.