Huy Fong Foods is the brand, sriracha is the product.
It's because he likes the fact that he created a new condiment and is satisfied with his current wealth and business size.
So if a competitor is selling red hot sauce in a bottle shaped just like a Huy Fong Sriracha bottle, along with similar writing, Huy Fong might have a case for challenging that, regardless of whether the competing product says "Sriracha" on it or displays the symbol of a rooster.