The short answer is "No." You can be a great parent by simply supporting your child's chess progress.
Knowing some things about chess will help reduce confusion. A lot of parents find their child's interest in chess begins to kindle their own. Maybe you've played casually at an early stage of life or maybe you've always wanted to learn. Having your child teach you can be a great way to help reinforce his or her own understanding. I've even known chess Dads to sneak study time with chess books to stay a few steps ahead of their progeny!