No. ESTA is processed electronically, so you do not have to print your approval before boarding.
Travelers are not required to bring a printed copy to the airport.
However, it is still helpful to keep a copy of the approval result for your own records.
It can be useful if you need to check your application number or confirm your approval status again.
In other words, print ESTA approval is not mandatory.
Even so, keeping either a printed copy or a digital copy is a practical way to prepare for travel.