It is not mandatory to purchase the Cinque Terre Card to have access to the Cinque Terre National Park.
The Cinque Terre Trekking Card is useful if you want to access the 2 paid trails in the park from Monterosso to Vernazza and from Vernazza to Corniglia. For the other paths you don't have to pay.
If you want to use the train several times with the option of trails in addition, it is better to buy the Cinque Terre MS Treno Card (CT Train Card).
For more information on the types of Cinque Terre Card tickets and prices, visit the page Cinque Terre Card.