You're probably right, my 7 year old son plays our games with us regularly (with adult supervision) and understands them and loves them. Boardgaming is in his blood. :)
There is a very good reason for this, and that reason is product safety. Products labeled for customers under the age of 13 (14 in some countries) are subject to stricter standards and testing which can be very expensive, and the liability in implying that we have made a product that is meant to be used by children without adult supervision can lead to lawsuits, which can also be very expensive.
Knowing that we produce games with very small parts and cannot personally oversee every step of the manufacturing process with our own eyes, it is safer for everyone's sake for us to package and label our products for players ages 14 and up. Under adult supervision however, we have no reason to suspect that our products are unsafe for anyone and have not cut any corners in the manufacturing process to include anything that would present a clear and deliberate danger to anyone.
Family time is very important to us and if you choose to include younger players, we encourage you to exercise your right to make the right decisions for your own unique situation. Thank you for your understanding and enjoy gaming time!