Indeed, Aerogel is legit. As its name implies it is a gel in which liquid vesicles were replaced with air bubbles. Hence its foam like properties; very voluminous yet very light.
Now let's proceed to read the gobbledygook at the link you provided.
Aerogel < It has strength up to 4,000 times its own weight> What does this mean? Strength is defined in terms of force per unit of length or per surface. Weight is a measure of the force with which the earth attracts an object. Can you say that an iron bar has x times the strength of its own weight? Not if you attended eighth grade science classes. Or that a pencil has x times the strength of its own weight?
<Aerogel's nanometer-sized molecular network> duh... Molecular networks are at nanometer scale. Saying nanometer-sized molecular network is as saying molecular sized molecular networks, or mice sized mice, or golf ball size golf balls.
<Aerogel racquets offer incredible power with touch and feel without compromising weight> Non-quantifiable nor verifiable statements. How many watts is incredible power? Without compromising weight? As opposed to the kind of touchy-feely stuff that tends to be weight compromising?
Pretty much all the descriptions provided are laughable and make for good entertainment. They would make good material to lighten up the mood in high school science class. Grammar and syntax are also lacking, as written by someone with only introductory level English.
Therefore I am asking; does this make you confident that the technologies are what they are purported to be?