No. You do not need a Beyond Body app subscription to obtain or use a MyBody subscription.
Beyond Body and MyBody are two separate apps and subscriptions.
What this means for you
You can purchase and use MyBody on its own, without having the Beyond Body app.
You can have both Beyond Body and MyBody at the same time.
Each app requires its own subscription and is managed separately.
Access to one app does not depend on having the other.
Important to know
Purchasing Beyond Body does not automatically include MyBody.
Purchasing MyBody does not automatically include Beyond Body.
There is no data syncing between the two apps.