Currency is a medium of exchange that confers purchasing power in a single set of markets, usually operating within a single national territory. A gift card is a medium of exchange that confers purchasing power at a a single business establishment, including possibly a scattered chain of franchises.
The fact that you purchase a gift card with another medium of exchange doesn’t mean that the gift card is not itself a medium of exchange. For example, I could use dollars to buy some Thai baht, and then give somebody the baht, which will then be accepted in mainly, though not exclusively, Thailand-based markets. I can also use the dollars to buy a Starbucks gift card, which they can then use only in Starbucks stores. The differences are only a matter of degree, having to do with the size and range of the market in which the medium will be accepted, not kind.
Gift cards are transferable and inheritable. And they can be traded for money.
Use “in trade” is just a kind of market exchange. If somebody gives me a puppy and I exchange it for some clothes, that is not an activity different in kind from receiving dollars, and exchanging them for clothes. In both cases, I am making a market decision and engaging in a market exchange.
I don’t know why the Buddha forbade the handling of money, but I suspect what he was doing was trying to restrict the element of economic choice among the monks. He wanted monastics to take what is given, and not to be making market exchange decisions themselves. I imagine that if a monk receives food in his bowl at one house, and then goes to a second house and exchanges that first gift of food for his choice from among some selection of other foods, that is not approved? Receiving money to be used for a latter exchange is like this. The difference seems to be only that, in the first case, the violation only occurs when the initially received food, which could have been eaten, is exchanged for other food. In the case of money, which cannot be eaten or personally used at all for anything other than a later exchange, he thought monks should’t take it in the first place.
Receiving the gift card seems more like the case of receiving money, since the card cannot itself be eaten or worn.
I assume the Buddha’s focus was on the kind of economic activity involved. He didn’t want monks involved in market exchange. It wouldn’t matter whether the money they received was made out of gold and silver, paper, tree bark, cigarettes, clam shells or balance quantities in electronic accounts. And he didn’t want them acquiring commodities for use in trade, or even for personal use beyond a limited number of purposes requisite for the maintenance of life and health.
Nevertheless, there are gross and lesser degrees of deviation from the highest ideal.