Arguably, they'll be happier with the video game than with a tank of gas, which you've ensured they'll choose by not giving them the cash

Edit to add: kids often don't have bank accounts, i mostly received gift cards as a child, from relatives who wouldn't want to mail cash and couldn't give me cash in person. On a dark note, giving a kid a gift card to a toy store makes it harder for the parents to steal it for themselves.

The whole practice originates from "gift certificates" where you'd maybe go to your favorite spa and get a gift certificate to give someone, so that the spa treatment is the gift you're giving, but the recipient redeems it whenever they want. That just got abstracted to non-service gifts as well, with the same idea ("treat yourself to a new video game, whichever and whenever you feel like it" -- that's the gift, facilitated by the card)

Also for kids at least, sometimes they really will be happier with less choice. Sometimes kids make bad decisions and limiting choice to good options is helpful.

Additionally the inverse is true. Sometimes kids choices are restrained, and they really would like to do a thing they are not allowed to, and gift cards offered them away to do that. Case in point: my tween figured out that we don’t let him buy in game currency for any the games that we do let him play, however, when a relative gives him a gift card, we let him redeem it, making gift cards incredibly popular gifts.